On Nonlinear Fractional Klein Gordon Equation


Asad Freihat. Gepreela)b)† and Mohamed S. Sections 5 and 6 are devoted to describe the negative frac-tional probability density situation and the physically acceptable conditions. Further, exact solutions of. Wavelet analysis is a recently developed mathematical tool in applied mathematics. Under suitable assumption on the potential, we establish the existence and uniqueness of the ground state solution. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method. UNSTABLE GROUND STATE OF NONLINEAR KLEIN-GORDON EQUATIONS BY JALAL SHATAH Abstract. 2 we have shown the graphs of u(x,t) corresponding @a uðx,tÞ @2 u to the values a ¼ 0:01, 0:5 and 1. Vong, A compact difference scheme for a two dimensional nonlinear fractional Klein-Gordon equation in polar coordinates, Comput. wave equation (where the relevant nonlinear object is the stationary function W whichsolves 1+4W+ W =(d 2) = 0). 2 Nonlinear Klein-Gordon equations EJDE{2002/26 The interaction of with the electro-magnetic eld is described by the min-imal coupling rule, that is the formal substitution @ @t 7! @ @t + ie˚ (1. Since then, this equation has been known as the Klein{Gordon equation. Abstract: We obtain solutions of the nonlinear Klein-Gordon equation using a novel operational method combined with the Adomian polynomial expansion of nonlinear functions. On the application of Ateb-functions to the construction of an asymptotic solution of the perturbed nonlinear Klein-Gordon equation | Springer for Research & Development. The FRDTM has several advantages for dealing directly with suggested equations; it needs a few iterations to get high accuracy, it is very simple for obtaining analytical-approximate solutions in rapidly convergent formulas, it. The properties of the Chebyshev polynomials are used to re-duce FKGE to the solution of system of ordinary differential equations which solved by using the finite difference method. top Small data scattering for nonlinear Schrödinger equations (NLS), nonlinear wave equations (NLW), nonlinear Klein-Gordon equations (NLKG) with power type nonlinearities is studied in the scheme of Sobolev spaces on the whole space ℝ n with order s < n / 2. Ghany and Mohamed S. Some results on the nonlinear Klein-Gordon-Maxwell equations Alessio Pomponio Dipartimento di Matematica, Politecnico di Bari, Italy Granada, Spain, 2011. In this paper, we apply two decomposition methods, the Adomian decomposition method (ADM) and a well-established iterative method, to solve time-fractional Klein–Gordon type equation. Skip to main content Search the history of over 380 billion web pages on the Internet. By the aid of a suitable generalization of the weighted Sobolev spaces we define the weighted Sobolev spaces on the upper branch of the unit hyperboloid. 2 we have shown the graphs of u(x,t) corresponding @a uðx,tÞ @2 u to the values a ¼ 0:01, 0:5 and 1. By using symbolic computation, we apply Auxiliary equation method to construct exact solutions of Non-Linear Klein-Gordon equation. Randomized exponential integrator for modulated nonlinear Schrödinger equations (preprint 2018) K. It is used to model many different phenomena, including the propagation of dislocations in crystals and the behaviour of elementary particles. The Local Fractional Series Expansion Method In order to illustrate the idea of the local fractional series expansion method [ ], we consider the local fractional di erential operator equationin the following form: 2 2= , (). Ebrahimizadeh 1Department of Mathematics, Fandanesh Institute of Higher Education (FDIHE), Saveh, 39157-14774, Iran. It would be very useful to carry out a systematic study on J-GL-C method with general indexes (θ,ϑ>−1). Vortex rings, spirals, and other solutions are demonstrated. , Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method, Advances in Difference Equations, 2012. Also, the nonlinear Klein-Gordon equation appears as a relativistic generalization of the Gross-Pitaevskii equation, a nonlinear Schr odinger equation that serves as a basic model for Bose-Einstein Condensates [2], also in the rotating case, see e. In this paper, we consider the fractional nonlinear Klein-Gordon equation where u is a function of x and t, a and b are real, g is a nonlinear function, and f is a known analytic function. The case where the Klein-Gordon equation is non-linear while solution amplitude tends to zero leads to the solutions localization in a spherically symmetric case. The main theme of this paper is the construction of symmetric and arbitrarily high-order time-stepping numerical methods for the nonlinear Klein{Gordon equa-tion and the analysis of their. methods for solving nonlinear fractional Klein-Gordon equation. Sunagawa, Large time behavior of solutions to the Klein–Gordon equation with nonlinear dissipative terms, J. Multi-solitons for nonlinear Klein-Gordon equations - Volume 2 - RAPHAËL CÔTE, CLAUDIO MUÑOZ Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. [27] Hossam A. A wavelet method for a class of space-time fractional Klein–Gordon equations with constant coefficients is proposed, by combining the Haar wavelet and operational matrix together and efficaciously dispersing the coefficients. Klein-Gordon equations (KGEs) by replacing the time order derivative with fractional derivative of order. GONZALEZ´ Abstract. The nonlinear Klein-Gordon equation is Utt - v2u + pu = f(lu12u). First, we provide an alternative proof of the stability of multibreathers in a chain with nearest neighbor interactions only. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method. Bournaveas and T. 10, 1127-1140. In particular the Payne-Sattinger dichotomy for solutions with energy less than that of the ground state, the Bates and Jones approach to the construction of Invariant Manifolds for semilinear partial di↵erential equations and the recent. We also prove the global well-posedness for the discrete Klein–Gordon equation, show the instability of the peakon solution, and the possibility of a formation of a breathing peakon. Using undetermined coefficient method we obtain bounded exact periodic wave solutions in fractional form of Jacobi elliptic function for Klein-Gordon equations which has nonlinear terms of five orders. Inspired by the paper of Donninger-Schlag on this equation, we further investigate the blow up and scattering behavior of its solutions. Global solutions of nonlinear wave–Klein–Gordon system in one space dimension states for fractional. Gepreel a b , Mohamed S. The nonrelativistic-semiclassical limit is proved rigorously by modulated energy method. Consequently, GKM has been implemented to find exact solutions of nonlinear time-fractional Klein-Gordon equation and we obtain some new solutions such as soliton solutions and hyperbolic function solutions. On the other hand the Klein-Gordon equation plays a significant role in several real world applications, for example, the solid state physics, nonlinear optics. Spectral Approximations for Nonlinear Fractional Delay Diffusion Equations with Smooth and Nonsmooth Solutions Liu, Haiyu, Lü, Shujuan, and Chen, Hu, Taiwanese Journal of Mathematics, 2019; On the Cauchy problem for the nonlinear Klein-Gordon equation with a cubic convolution Motai, Takahiro, Tsukuba Journal of Mathematics, 1988. We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. nonlinear Klein-Gordon equation in three dimensions. We recall that (1. By the aid of a suitable generalization of the weighted Sobolev spaces we define the weighted Sobolev spaces on the upper branch of the unit hyperboloid. In this work, we investigate numerically a nonlinear hyperbolic partial differential equation with space fractional derivatives of the Riesz type. Crossref Google Scholar. Laguerre collocation method is presented for solving linear fractional Klein-Gordon equation (LFKGE). It is proved that, both the governing equations are stable. Nonlinear Analysis: Modelling and Control, 2015, Vol. Discrete & Continuous Dynamical Systems - A , 2020, 40 (1) : 597-608. Abstract— Reduced differential transform method (RDTM) is implemented for solving the linear and nonlinear Klein Gordon equations. On the Energy decay of the Damped Klein-Gordon and Fractional Damped Klein-Gordon Equations, SIAM Conference on Nonlinear Wave and Coherent Structures, Orange (California), June 11-14, 2018, ( Contributed talk) When is the energy of the 1D damped Klein-Gordon equation decaying?SIAM Conference (Baltimore)Dec 8-Dec 11-2017 (Invited talk). of the nonlinear Klein-Gordon equation (1. The fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space—time fractional derivatives Klein—Gordon equation. 2012 (2012), No. 1993 Dec;48(6):4768-4778. The approximate solutions of the fractional equation are based on cubic B-spline collocation finite element method and L2 algorithm. By the aid of a suitable generalization of the weighted Sobolev spaces we define the weighted Sobolev spaces on the upper branch of the unit hyperboloid. The homotopy perturbation method (HPM) has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation which can be used as a numerical algorithm []. The fractional derivative is described in Caputo sense. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation can be used as numerical algorithm. By using this method, we found some new traveling wave solutions of the above-mentioned equation. Schratz, X. Baumstark, G. The Dual Reciprocity Boundary Integral Equation Technique to Solve a Class of the Linear and Nonlinear Fractional Partial Differential Equations, Math. Author of [27] investigated three different finite differ-ence approximations of the initial nonlinear Klein-Gordon equa-tion, showed they are directly related to symplectic mappings and. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation can be used as numerical algorithm. We show that the energy of the solution. The method has been successively provided for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation. fractional coupled Klein-Gordon-Schrdinger equations, which does not require a small parameter inthe equations. Some results on the nonlinear Klein-Gordon-Maxwell equations Alessio Pomponio Dipartimento di Matematica, Politecnico di Bari, Italy Granada, Spain, 2011. In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Local well-posedness for the spacetime Monopole equation in Lorenz gauge, Nonlinear Diff. solutions for linear Klein-Gordon equations on Cantor sets are presented. A linearized scheme is proposed to solve the problem. 1 Introduction The coupled Klein-Gordon-Schrodinger (KGS) system is a classical model in quantum¨ mechanics, which describes the Yukawa interaction between the conservative complex. In this paper we obtain some non-existence results for the Klein-Gordon equation coupled with the electrostatic field. (2011)) introduced a new approximate formula of the fractional derivative and used it to solve numerically the fractional diffusion equation. There are many powerful numerical methods that have been applied in order to solve the nonlinear Klein-Gordon equation. Nosrati Sahlan 2, and A. Residual power series algorithm gets Maclaurin expansion of the solution. Sterbenz, Global Stability for Charged Scalar Fields on Minkowski. A system of two hyperbolic equations describing the interaction of a complex nucleon field with a real meson field is considered in a domain of $\mathbb{R}^n $, $n. Bellazzini, V. Vortex rings, spirals, and other solutions are demonstrated. In this paper, numerical solution of non‐linear Klein-Gordon equations with power law non‐linearities are obtained by the new application of He's variational iteration method. The fundamental idea of the Haar wavelet method is to convert the fractional Klein–Gordon equations into a group of algebraic equations, which involves a. Bournaveas and T. Stefanov, Communications in Pure and Appl. Introduction. Additionally, inter-site centered peakons are also obtained in explicit form and their stability is studied. It is observed that suggested scheme is highly reliable and may be extended to other nonlinear differential equa-tions of fractional order. Demo - Cubic nonlinear Klein-Gordon equation¶ Authors. Our analysis relies on a detailed study of the spectral properties of the linearization of the equation, and on the well-known 'slope condition' for orbital stability. 3) because of its analogue to the nonlinear Schr odinger equation (1. This paper extends the homotopy perturbation Sumudu transform method (HPSTM) to solve linear and nonlinear fractional Klein-Gordon equations. On The Solutions of Nonlinear Fractional Klein-Gordon Equation by Means of Local Fractional Derivative Operators 20 In this paper, we extend the application of the LFDM to derive the analytical approximate solutions of the nonlinear. Residual power series algorithm gets Maclaurin expansion of the solution. In this paper, we apply two decomposition methods, the Adomian decomposition method (ADM) and a well-established iterative method, to solve time-fractional Klein–Gordon type equation. 2 The Sine-Gordon equation 2. The mechanisms discussed are local inertial forces (Coriolis and centrifugal), and current-current interaction with an external source. Author of [27] investigated three different finite differ-ence approximations of the initial nonlinear Klein-Gordon equa-tion, showed they are directly related to symplectic mappings and. On the other hand the Klein-Gordon equation plays a signi cant role in several real world applications, for example, the solid state physics, nonlinearoptics, and quantum eld theory. The fractional derivatives are described in the Caputo sense. Further, exact solutions of. This video is unavailable. The properties of the Chebyshev polynomials are used to re-duce FKGE to the solution of system of ordinary differential equations which solved by using the finite difference method. 1), it is better to start from (1. The Klein-Gordon equation plays an important role in mathematical physics. construct generalized solitary wave solutions of the nonlinear Klein-Gordon equations of fractional-order. The Mathematical Modelling of Natural Phenomena (MMNP) is an international research journal, which publishes top-level original and review papers, short communications and proceedings on mathematical modelling in biology, medicine, chemistry, physics, and other areas. Due to the Klein-Gordon equation's enormous popularity, the SGE was named so as a wordplay. Home > Journal of the Physical Society of Japan > Volume 52, Number 11 > On Soliton Solutions of the Nonlinear Coupled Klein-Gordon Equation J. Blow up and scattering sets in the non linear Klein-Gordon equation Par Svetlana Roudenko (George Washington University) Dans le cadre de la Chaire d'Excellence de Nader Masmoudi (Courant Institute of Mathematical Sciences) - accueilli au LAGA. Three types of TFND partial differential equations are considered in the sense of CFD, which are the TFND Boussinesq, TFND Klein-Gordon, and TFND B (2, 1, 1) PDEs. The FRDTM has several advantages for dealing directly with suggested equations; it needs a few iterations to get high accuracy, it is very simple for obtaining analytical-approximate solutions in rapidly convergent formulas, it. Klein-Gordon equations (KGEs) by replacing the time order derivative with fractional derivative of order. We study the asymptotic behavior of the semilinear Klein-Gordon equation with nonlinearity of fractional order. A numerical method based on collocation points was developed in ]7[ to solve the nonlinear Klein-Gordon equations by using the Taylor matrix method. nonlinear Klein–Gordon equation and discuss their relation to the compressible and incompressible Euler equations. Nonlinear Klein-Gordon equation and its application on f(R) theory of gravitation. construct generalized solitary wave solutions of the nonlinear Klein-Gordon equations of fractional-order. In the last decades Iterative methods have been used for solving fractional differential equations. Samraiz Department of Mathematics University of Sargodha Sargohda, pakistan [email protected] We study the asymptotic behavior of the semilinear Klein-Gordon equation with nonlinearity of fractional order. Demo - Cubic nonlinear Klein-Gordon equation¶ Authors. First, we provide an alternative proof of the stability of multibreathers in a chain with nearest neighbor interactions only. The proposed method is easy, direct and concise as compared with other existent methods. It is observed that suggested scheme is highly reliable and may be extended to other nonlinear differential equa-tions of fractional order. We obtain exact solutions to the space-time fractional Eckhaus equation and the space-time fractional generalized reaction Duffing model with sine-Gordon expansion method in Sect. Keywords: First Integral Method, Exact Solution, Fractional Klein-Gordon. Mohamed, Analytical approximate solution for nonlinear space-time fractional Klein Gordon equation, Chinese physics B, Vol. Abstract— Reduced differential transform method (RDTM) is implemented for solving the linear and nonlinear Klein Gordon equations. Watch Queue Queue. This paper extends the homotopy perturbation Sumudu transform method (HPSTM) to solve linear and nonlinear fractional Klein-Gordon equations. By using symbolic computation, we apply Auxiliary equation method to construct exact solutions of Non-Linear Klein-Gordon equation. In this paper, we implement the spectral collocation method with the help of the Legendre poly-nomials for solving the non-linear Fractional (Caputo sense) Klein-Gordon Equation (FKGE). Vortex rings, spirals, and other solutions are demonstrated. title = "Scattering threshold for the focusing nonlinear Klein-Gordon equation", abstract = "We show scattering versus blow-up dichotomy below the ground state energy for the focusing nonlinear Klein-Gordon equation, in the spirit of Kenig and Merle for the H1 critical wave and Schr{\"o}dinger equations. of the modulated defocusing nonlinear Klein‐Gordon equation is the defocus‐ ing nonlinear Schrödinger equations. linear fields on the Schwarzschild geometry : the non linear Dirac equation, Yang-Mills fields and non linear Klein-Gordon fields were studied respectively by A. evolution equation, we show that both the classical Schro¨dinger and Klein-Gordon equations can be viewed as a consequence of introduc-ing a memory function given by −iδ and δ(1), respectively. pdf Berestycki H. The Green function method combined with integral transforms is employed to solve the linear Klein-Gordon equation. The proposed method is easy, direct and concise as compared with other existent methods. Stefanov, Communications in Pure and Appl. The obtained results reveal that these methods are very accurate and effective. 2, 274-290 Efficient high-order finite difference methods for nonlinear Klein-Gordon equations. Ebrahimizadeh 1Department of Mathematics, Fandanesh Institute of Higher Education (FDIHE), Saveh, 39157-14774, Iran. 1) is the Euler-Lagrange equation with respect to the La-grangian density L NLKG. In this paper, the homotopy analysis method is applied to obtain the solution of nonlinear fractional partial differential equations. The homotopy perturbation method (HPM) has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation which can be used as a numerical algorithm. Fractional Klein-Gordon equation has been studied by many researchers for instance, homotopy perturbation method by Baleanu et al [25, 26], and approximate analytical solution for linear and. It covers Pade approximation theory, embedded-parameters perturbation, Adomian decomposition, homotopy analysis, modified differential transformation, fractal theory, fractional calculus, fractional differential equations, as well as classical numerical techniques for solving nonlinear partial differential equations. Consequently, GKM has been implemented to find exact solutions of nonlinear time-fractional Klein-Gordon equation and we obtain some new solutions such as soliton solutions and hyperbolic function solutions. In this article, a general formula of the first integral method has been extended to celebrate the exact solution of nonlinear time-space differential equations of fractional orders. and Satbir Malhi. [PRESENTATION IN VIDEO] American Control Conference 2006, 6. title = "Scattering threshold for the focusing nonlinear Klein-Gordon equation", abstract = "We show scattering versus blow-up dichotomy below the ground state energy for the focusing nonlinear Klein-Gordon equation, in the spirit of Kenig and Merle for the H1 critical wave and Schr{\"o}dinger equations. fractional Klein-Gordon equation, §3 and 4 are used to derive the fractional Klein-Gordon equation and fractional equation of continuity, respectively. Browse other questions tagged homework-and-exercises lagrangian-formalism conservation-laws noethers-theorem klein-gordon-equation or ask your own question. In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. The mechanisms discussed are local inertial forces (Coriolis and centrifugal), and current-current interaction with an external source. Author of [27] investigated three different finite differ-ence approximations of the initial nonlinear Klein–Gordon equa-tion, showed they are directly related to symplectic mappings and. On the Energy decay of the Damped Klein-Gordon and Fractional Damped Klein-Gordon Equations, SIAM Conference on Nonlinear Wave and Coherent Structures, Orange (California), June 11-14, 2018, ( Contributed talk) When is the energy of the 1D damped Klein-Gordon equation decaying?SIAM Conference (Baltimore)Dec 8-Dec 11-2017 (Invited talk). Bobenko, AI & Kuksin, S 1995, ' The nonlinear Klein-Gordon equation on an interval as a perturbed Sine-Gordon equation ', Commentarii Mathematici Helvetici, vol. By this method noise terms disappear in the iteration process and single iteration gives the exact solution. On the Cauchy problem for nonlinear Klein-Gordon equations in de Sitter spacetime Makoto Nakamura 1 We consider local and global energy solutions for the Cauchy problem of non-linear Klein-Gordon equations in de Sitter spacetime. Bilinear Estimates and applications to global well-posedness for the Dirac-Klein-Gordon equation, J. Read "Analytical and numerical validation for solving the fractional Klein-Gordon equation using the fractional complex transform and variational iteration methods, Nonlinear Engineering" on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. fractional order Klein–Gordon equations by using a recently developed semi analytical method referred as fractional reduced differential transform method with appropriate initial condition. This chapter deals with the theory and applications of nonlinear Klein-Gordon (KG) and sine-Gordon (SG) equations. A system of two hyperbolic equations describing the interaction of a complex nucleon field with a real meson field is considered in a domain of $\mathbb{R}^n $, $n. Muhammet Kurulay in [4] solve the fractional nonlinear Klein-Gordon equation by means of the homo- topy analysis method. We recall that (1. In this work we study the decay properties of the semilinear Klein-Gordon equation with nonlinearity of fractional order. Zimmermann:. Japan, 58 (2006), 379-400. From this end idea we introduce in this paper the concept of generalized. The main aim of this work is to apply the HPM to solve the nonlinear Klein-Gordon equations of fractional order. For example, nonlinear sine Klein–Gordon equation models a Josephson junction, the motion of rigid pendula attached to a stretched wire, and dislocations in crystals , , , ,. This is due to the fact that the solution becomes highly-oscillatory in time in this regime which causes the breakdown of classical integration schemes. Firstly, we use fractional traveling wave transformations to convert fractional nonlinear partial differential equations to nonlinear ordinary differential equations. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method. Browse other questions tagged homework-and-exercises lagrangian-formalism conservation-laws noethers-theorem klein-gordon-equation or ask your own question. A linearized scheme is proposed to solve the problem. It is observed that suggested scheme is highly reliable and may be extended to other nonlinear differential equa-tions of fractional order. (2017) A linearized, decoupled, and energy-preserving compact finite difference scheme for the coupled nonlinear Schrödinger equations. To illustrate the reliability of the method, some examples are presented. Parsian [5] introduced the two dimensional. Analytical approximate solution for nonlinear space-time fractional Klein–Gordon equation Khaled A. Introducing a new constraint minimization problem, we prove the existence of ground states for an associated stationary elliptic system. UROOSA2,x Abstract. Abstract: We obtain solutions of the nonlinear Klein-Gordon equation using a novel operational method combined with the Adomian polynomial expansion of nonlinear functions. Mohamed, White noise functional solutions for the wick-type stochastic fractional Kdv-Burgers-Kuramoto Equations, Journal. In these spaces of fractional order we obtain a weighted Sobolev embedding and a nonlinear estimate. Wavelet analysis is a recently developed mathematical tool in applied mathematics. Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method. Nonlinear fractional differential equations and inclusions of arbitrary order and multi-strip boundary conditions, Vol. In this paper we prove the instability of the ground state, i. Coupled systems of fractional differential inclusions with coupled boundary conditions , Vol. 4) r7!r ieA (1. Global solutions of nonlinear wave–Klein–Gordon system in one space dimension states for fractional. Special emphasis is given to various methods of solutions of these equations. SULTANA , F. The nonlinear fractional Klein-Gordon equation with quadratic nonlinearity reads as We notice that the nonlinear fractional Klein-Gordon equation describes many types of nonlinearities. In order to show the efficiency and accuracy of the mentioned method, we have applied it to time-fractional nonlinear Klein-Gordon equation. Well, it is true that by taking the square root of the equation you might get rid of the negative energy solutions that trouble physicists for several years. 1007/s12043-018-1673-3 Copy DOI. The FRDTM has several advantages for dealing directly with suggested equations; it needs a few iterations to get high accuracy, it is very simple for obtaining analytical-approximate solutions in rapidly convergent formulas, it. The homotopy perturbation method (HPM) has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation which can be used as a numerical algorithm []. By the aid of a suitable generalization of the weighted Sobolev spaces we define the weighted Sobolev spaces on the upper branch of the unit hyperboloid: (formula presented) In these spaces of fractional order we obtain a weighted Sobolev inequality and a nonlinear estimate. The fractional derivatives are presented in terms of the Caputo sense. The Legendre collocation method is used to reduce FKGE to the solution of system of ODEs which is solved by using finite difference method. On the other hand, solving differential equation with fractional derivative might be much. Schneider, K. From this end idea we introduce in this paper the concept of generalized. 3722-3726 (1983) [5 Pages]. Strichartz estimate and nonlinear Klein-Gordon equation on non-trapping scattering space for 2D fractional order Schrödinger operators Klein-Gordon Equation. The main aim of this work is to apply the HPM to solve the nonlinear Klein-Gordon equations of fractional order. @2w @t2 = @2w @x2 + f(w). The fractional derivative is described in Caputo sense. In the first part we construct a model which describes solitary waves of the nonlinear Klein-Gordon equation interacting with the electromagnetic field. A wavelet method for a class of space-time fractional Klein-Gordon equations with constant coefficients is proposed, by combining the Haar wavelet and operational matrix together and efficaciously dispersing the coefficients. Small data scattering for nonlinear Schrödinger equations (NLS), nonlinear wave equations (NLW), nonlinear Klein-Gordon equations (NLKG) with power type nonlinearities is studied in the scheme of Sobolev spaces on the whole space ℝ n with order s < n / 2. In this paper, the time-fractional nonlinear dispersive (TFND) partial differential equations (PDEs) in the sense of conformable fractional derivative (CFD) are proposed and analyzed. The case where the Klein-Gordon equation is non-linear while solution amplitude tends to zero leads to the solutions localization in a spherically symmetric case. The Dual Reciprocity Boundary Integral Equation Technique to Solve a Class of the Linear and Nonlinear Fractional Partial Differential Equations, Math. In the Appendices Nonlinear Klein Gordon equations with solitary (travelling) wave solutions are reviewed and solved for particular cases. On the other hand the Klein-Gordon equation plays a significant role in several real world applications, for example, the solid state physics, nonlinear optics. [FULL] Quantum optimal control of nonlinear dynamics systems described by Klein-Gordon-Schrodinger equations. Abstract: This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced Differential Transform Method (FRDTM). Analytical approximate solution for nonlinear space-time fractional Klein Gordon equation Khaled A. From this end idea we introduce in this paper the concept of generalized. nonlinear partial differential equations included some well-known fractional Klein-Gordon equations. By using symbolic computation, we apply Auxiliary equation method to construct exact solutions of Non-Linear Klein-Gordon equation. nonlinear Klein-Gordon equation in three dimensions. We obtain exact solutions to the space-time fractional Eckhaus equation and the space-time fractional generalized reaction Duffing model with sine-Gordon expansion method in Sect. We treat the nonlinear Klein-Gordon (NKG) equation as the Sine-Gordon (SG) equation, perturbed by a higher order term. In this paper we prove the instability of the ground state, i. time-fractional order linear and nonlinear Klein-Gordon equations. The fractional derivatives are described in the Caputo sense. 3722-3726 (1983) [5 Pages]. In the present paper, we couple double Laplace transform with Iterative method to solve nonlinear Klein-Gordon equation subject to initial and boundary conditions. We present results on multibreather stability in one-dimensional nonlinear Klein-Gordon chains. By the aid of a suitable generalization of the weighted Sobolev spaces we define the weighted Sobolev spaces on the upper branch of the unit hyperboloid: (formula presented) In these spaces of fractional order we obtain a weighted Sobolev inequality and a nonlinear estimate. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied. The primary application is to. @2w @t2 = @2w @x2 + f(w). Mohamed, Analytical approximate solution for nonlinear space-time fractional Klein Gordon equation, Chinese physics B, Vol. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. We construct time quasi-periodic solutions to the nonlinear Klein-Gordon equations on the torus in arbitrary dimensions. In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. In paper ]8[ the nonlinear one-dimensional Klein-Gordon equation was solved with the help of the. 2 Nonlinear Klein-Gordon equations EJDE{2002/26 The interaction of with the electro-magnetic eld is described by the min-imal coupling rule, that is the formal substitution @ @t 7! @ @t + ie˚ (1. SULTANA , F. The fractional derivative is considered in the Caputo sense. Four examples are provided to show the accuracy and coherence of the proposed technique. The method has been successively provided for finding approximate analytica Authors: Muhammet Kurulay. In this paper, we study a nonlinear Klein-Gordon equation coupled with a Maxwell equation. It would be very useful to carry out a systematic study on J-GL-C method with general indexes (θ,ϑ>−1). In this paper, a generalized Riccati equation method for obtaining exact solutions of nonlinear partial differential equationds is proposed and applied. A wavelet method for a class of space-time fractional Klein-Gordon equations with constant coefficients is proposed, by combining the Haar wavelet and operational matrix together and efficaciously dispersing the coefficients. By the aid of a suitable generalization of the weighted Sobolev spaces we define the weighted Sobolev spaces on the upper branch of the unit hyperboloid. For a memory function of the type i1+ ( ) where 0 < <1 we derive a fractional Schr odinger-Klein-Gordon equation whose corresponding. A linearized scheme is proposed to solve the problem. Mohamed, Analytical approximate solution for nonlinear space-time fractional Klein Gordon equation, Chinese physics B, Vol. The type of coupling depends on the type of the interface and constitutes an arbitrary element of the Lie group classification problem, which is solved for these equations. nonlinear Klein-Gordon equation which appears in nonlinear optics, plasma physics, and fluid me- chanics. It is shown that solutions of the nonlinear Klein-Gordon equation u tt - ∆ u + mu + P'(u) = 0 decay to zero in the local L 2 mean if the initial energy is bounded provided sP')s) - 2P(s) ≥ aP(s) ≥ 0 with a > 0. Muhammet Kurulay in [4] solve the fractional nonlinear Klein-Gordon equation by means of the homo- topy analysis method. The Green function method combined with integral transforms is employed to solve the linear Klein-Gordon equation. Let n ≥ 1, M > 0, H > 0, c > 0, and let us consider the Cauchy problem given by (@2. of the nonlinear Klein-Gordon equation (1. diffusion equation, Non linear parabolic equations, fractional Klein-Gordon equations, sine-Gordon equations and Fisher's equation. Signal Processing, 91, 446-451. Klein Gordon is related to a wave equation. In this article, a general formula of the first integral method has been extended to celebrate the exact solution of nonlinear time-space differential equations of fractional orders. Sections 5 and 6 are devoted to describe the negative frac-tional probability density situation and the physically acceptable conditions. We show that Auxiliary equation method provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. In this article, a novel variable order fractional nonlinear Klein Gordon model is presented where the variable‐order fractional derivative is defined in the Caputo sense. As a model for describing a rotating galaxy in Minkowski metric, the nonlinear Klein-Gordon equation in a rotating. We prove for such an equation that there is a neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. for a "cosmic superfluid". Randomized exponential integrator for modulated nonlinear Schrödinger equations (preprint 2018) K. The general framework is a nonlinear Klein-Gordon equation in curved spacetime for a complex scalar field, whose phase dynamics gives rise to superfluidity. Watch Queue Queue. 3) because of its analogue to the nonlinear Schr odinger equation (1. The most downloaded articles from Applied Numerical Mathematics in the last 90 days. finally, the tension spline approach for the numerical solution of nonlinear Klein-Gordon equation is implemented in (Rashidini & Mohammadi (2010)). It would be very useful to carry out a systematic study on J-GL-C method with general indexes (θ,ϑ>−1). It is proved that, both the governing equations are stable. Gepreel and M. The Dual Reciprocity Boundary Integral Equation Technique to Solve a Class of the Linear and Nonlinear Fractional Partial Differential Equations, Math. Then we presented an algorithm of the homotopy perturbation transform method to solve coupled Klein-Gordon-Schrdinger equations. Chowdhury and Hashim have employed HPM for solving Klein-Gordon equations. traveling wave solutions of non-linear evolution equations. com Abstract: This paper presents the formulation of time-fractional Klein-Gordon equation using the Euler-Lagrange. (2017) Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations. In this paper, we explore new application of this method to non-linear Klein-Gordon equation, the balance numbers of which are both positive and negative. We study the asymptotic behavior of the semilinear Klein-Gordon equation with nonlinearity of fractional order. By the aid of a suitable generalization of the weighted Sobolev spaces we define the weighted Sobolev spaces on the upper branch of the unit hyperboloid. The convergence of the HPSTM solutions to the exact solutions is shown. In this paper, we want to understand the dynamics of large, quantized energy. 5) where eis the electric charge. We obtain exact solutions to the space-time fractional Eckhaus equation and the space-time fractional generalized reaction Duffing model with sine-Gordon expansion method in Sect. , Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method, Advances in Difference Equations, 2012. The contributing authors represent a group of international experts in the field and discuss recent trends and new directions in nonlinear elliptic partial differential equations and systems. As a result, new exact travelling wave solutions are obtained. On the spectral stability of ground states of the semilinear Schr odinger and Klein-Gordon equations with fractional dispersion, joint with W. The aim of this work is to study the global existence of solutions for the Cauchy problem of a Klein-Gordon equation with high energy initial data. The mechanisms discussed are local inertial forces (Coriolis and centrifugal), and current-current interaction with an external source. As a result, iterative method need not be. On space-time means for solutions of nonlinear Klein-Gordon equations Doctoral thesis, 2003. Four examples are provided to show the accuracy and coherence of the proposed technique. 1186/1687-1847-2012-187. Feng and A. We prove for such an equation that there is a neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. Finally, we suggest a method of finding travelling wave solutions of the nonlinear fractional Klein-Gordon equation with power law. On the application of Ateb-functions to the construction of an asymptotic solution of the perturbed nonlinear Klein-Gordon equation | Springer for Research & Development. The purpose of this paper is to consider the time-splitting Fourier spectral (TSFS) method to solve the fractional coupled Klein-Gordon-Schrödinger (K-G-S) equations. The homotopy perturbation method (HPM) has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation which can be used as a numerical algorithm []. Wavelet Galerkin Method for the Solution of Nonlinear Klein-Gordon Equations By Using B-Spline Wavelets K.