## On Nonlinear Fractional Klein Gordon Equation

Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. Demo - Cubic nonlinear Klein-Gordon equation¶ Authors. title = "The method of lines and the nonlinear Klein-Gordon equation",. Browse other questions tagged homework-and-exercises lagrangian-formalism conservation-laws noethers-theorem klein-gordon-equation or ask your own question. 73 (2005), no. 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. Diﬀerential equations involving fractional order derivatives are used to model a variety of systems, of which the im-. Recently published articles from Nonlinear Analysis. Nonlinear Analysis: Modelling and Control, 2015, Vol. Next, the modified Kudryashov method is applied to find exact solutions of these equations. We consider the fractional Klein-Gordon equation in one spatial dimension, subject to a damping coe cient, which is non-trivial and periodic, or more generally strictly positive on a periodic set. In the first part we construct a model which describes solitary waves of the nonlinear Klein-Gordon equation interacting with the electromagnetic field. Parsian  introduced the two dimensional. There are many powerful numerical methods that have been applied in order to solve the nonlinear Klein-Gordon equation. Nonlinear Klein-Gordon Equation Necat Polata, Hatice Taskesenb aDepartment of Mathematics, Dicle University, 21280, Diyarbakir bDepartment of Statistics, Yuzuncu Yil University, 65080, Van Abstract. nonlinear Klein–Gordon equation with Dirichlet boundary condi-tion on a bounded domain, which shows the overﬂow solution as expected. The coupled nonlinear KG types equation will be collocated only for the space vari-. 1), it is better to start from (1. We consider numerics / asymptotics for the rotating nonlinear Klein-Gordon (RKG) equation, an important PDE in relativistic quantum physics that can model a rotating galaxy in Minkowski metric and serves also as a model e. We study the nonrelativistic, semiclassical and nonrelativistic- semiclassical limits of the (modulated) nonlinear Klein-Gordon equations from its hydrodynamical structure via WKB analysis. 2461-2476, 2016. The fractional derivative is considered in the Caputo sense. In paper ]8[ the nonlinear one-dimensional Klein-Gordon equation was solved with the help of the. 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. We present an approximate formula of the fractional derivative. It is observed that suggested scheme is highly reliable and may be extended to other nonlinear differential equa-tions of fractional order. By using this method, we found some new traveling wave solutions of the above-mentioned equation. We prove that the non-radial sign-cha. We compare these methods and discuss the convergence of them. We study the asymptotic behavior of the semilinear Klein-Gordon equation with nonlinearity of fractional order. On the basis of our solutions we discuss various nonhomogeneous patterns, which can be formed at the critical point of systems described by the. A satisfier function that satisfies all the initial and boundary conditions was used. 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. Moreover, the stability for the governing equations is investigated via the aspect of linear stability analysis. Klein-Gordon equation (FKGE). Golmankhaneh, A. In the last decades Iterative methods have been used for solving fractional differential equations. On Global Attraction to Solitary Waves for the Klein-Gordon Equation Coupled to Nonlinear Oscillator by Alexander Komech; Andrew Komech. Mohamed b c a Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt;. Abstract— Reduced differential transform method (RDTM) is implemented for solving the linear and nonlinear Klein Gordon equations. Nonlinear Klein-Gordon Equation Necat Polata, Hatice Taskesenb aDepartment of Mathematics, Dicle University, 21280, Diyarbakir bDepartment of Statistics, Yuzuncu Yil University, 65080, Van Abstract. Eman Abuteen. The general framework is a nonlinear Klein-Gordon equation in curved spacetime for a complex scalar field, whose phase dynamics gives rise to superfluidity. 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. In the present paper, we couple double Laplace transform with Iterative method to solve nonlinear Klein-Gordon equation subject to initial and boundary conditions. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. In this paper we obtain some non-existence results for the Klein-Gordon equation coupled with the electrostatic field. 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 []. maybe try This is a nonlinear Klein-Gordon equation of the type On the fractional Schrödinger equation. In the study of fractional Klein-Gordon equation, fractional derivative is described in the Caputo sense. diffusion equation, Non linear parabolic equations, fractional Klein-Gordon equations, sine-Gordon equations and Fisher's equation. , Stable solutions of the logarithmic Schrödinger equation, Nonlinear Anal. Aug 23, 2019. Feng and A. General Mathematics [math. Fractional Klein Gordon Equation ABSTRACT In the present manuscript, a new numerical scheme is presented for solving the time fractional nonlinear Klein-Gordon equation. least energy steady-state solution of nonlinear Klein-Gordon equations with space dimension n » 3. We present an approximate formula of the fractional derivative. traveling wave solutions of non-linear evolution equations. Inspired by the paper of Donninger-Schlag on this equation, we further investigate the blow up and scattering behavior of its solutions. Stability and convergence are analyzed using the matrix form of the scheme. Introduction The Klein-Gordon equation is a relativistic version of the Schrödinger equation describing free particles, which was proposed by Oskar Klein and Walter Gordon in 1926. The Dual Reciprocity Boundary Integral Equation Technique to Solve a Class of the Linear and Nonlinear Fractional Partial Differential Equations, Math. Let n ≥ 1, M > 0, H > 0, c > 0, and let us consider the Cauchy problem given by (@2. On Global Attraction to Solitary Waves for the Klein-Gordon Equation Coupled to Nonlinear Oscillator by Alexander Komech; Andrew Komech. (2018) A fast second-order implicit scheme for non-linear time-space fractional diffusion equation with time delay and drift term. In the compact case, we establish existence of traveling wave solutions via energy minimization methods and prove that at least compact isotropic manifolds have genuinely traveling waves. Mohamed b c a Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt;. Klein-Gordon equation (FKGE). Baumstark, G. Their combined citations are counted only for the first article. On the basis of our solutions we discuss various nonhomogeneous patterns, which can be formed at the critical point of systems described by the. 2, 345{35 27. 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. methods for obtaining exact solutions for nonlinear 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. [FULL] Quantum optimal control of nonlinear dynamics systems described by Klein-Gordon-Schrodinger equations. Then we presented an algorithm of the homotopy perturbation transform method to solve coupled Klein-Gordon-Schrdinger equations. For the defocusing nonlinear Schr odinger equation, the semiclassical limit for initial data with Sobolev regularity in short time has been studied by Gre-nier . It got a lot of attention for studying solitons and condensed matter physics (Yusufoglu, 2008;. (2017) Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations. The method has been successively provided for finding approximate analytica Authors: Muhammet Kurulay. This work is motivated by the investigation of a fractional extension of a general nonlinear multidimensional wave equation with damping. nonlinear Klein–Gordon equation with Dirichlet boundary condi-tion on a bounded domain, which shows the overﬂow solution as expected. The phase portraits of the solutions are also given. We consider the fractional Klein-Gordon equation in one spatial dimension, subject to a damping coe cient, which is non-trivial and periodic, or more generally strictly positive on a periodic set. Firstly, we use fractional traveling wave transformations to convert fractional nonlinear partial differential equations to nonlinear ordinary differential equations. Differential Equations 10 (2013), no. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota. Thus, the main purpose of this paper is to present the rst step towards a general theory. The properties of Laguerre polynomials are utilized to reduce LFKGE to a system of ordinary differential equations, which solved using the ﬁnite difference method. To illustrate the reliability of the method, some examples are presented. Global solutions of nonlinear wave–Klein–Gordon system in one space dimension states for fractional. , Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method, Advances in Difference Equations, 2012. Nonlinear Analysis: Modelling and Control, 2015, Vol. The phase portraits of the solutions are also given. On nonlinear fractional Klein-Gordon equation. Strichartz estimate and nonlinear Klein-Gordon equation on non-trapping scattering space for 2D fractional order Schrödinger operators Klein-Gordon Equation. Fractional Klein-Gordon equation has been studied by many researchers for instance, homotopy perturbation method by Baleanu et al , , and approximate analytical solution for linear and nonlinear time fractional order Klein-Gordon equations by Tamsir and Srivastava. 1, 2 Index Terms-- the space-time fractional foam drainage equation; space-time fractional Klein Gordon equation; the modified Kudryashov method. 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. In this paper, a generalized Riccati equation method for obtaining exact solutions of nonlinear partial differential equationds is proposed and applied. and Satbir Malhi. Laguerre collocation method is presented for solving linear fractional Klein-Gordon equation (LFKGE). v7 Uk 3Q Tx 5T BI Bu y7 BE zu x9 N2 Eq Vo Zg 00 Yz QV M6 Cj 5f 2h 9c 9M sL 5J wD JR qp Tl Zi l8 jJ mc 64 0B uK Vo ya 2R xr rI qY UG vB GZ hy o3 i7 T1 S4 VI 0D An Yv. 2 The Sine-Gordon equation 2. Under suitable assumption on the potential, we establish the existence and uniqueness of the ground state solution. It would be very useful to carry out a systematic study on J-GL-C method with general indexes (θ,ϑ>−1). Mikael Mortensen (mikaem at math. Our analysis is based on Aubry's band theory and perturbation theory. We study the asymptotic behavior of the semilinear Klein-Gordon equation with nonlinearity of fractional order. 3722-3726 (1983) [5 Pages]. 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. 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. Special emphasis is given to various methods of solutions of these equations. 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. Some results on the nonlinear Klein-Gordon-Maxwell equations Alessio Pomponio Dipartimento di Matematica, Politecnico di Bari, Italy Granada, Spain, 2011. We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. We investigate the kink solutions to the generalized nonlinear Klein-Gordon equation. Demo - Cubic nonlinear Klein-Gordon equation¶ Authors. and Klein-Gordon equations: Given an appropriate structure of the space at in n-ity and given that the location of the resonances ts well with the non-linear terms, see the discussion below, one can solve (suitable) semilinear equations. A Novel Method to Solve Nonlinear Klein-Gordon Equation Arising in Quantum Field Theory Based on Bessel Functions and Jacobian Free Newton-Krylov Sub-Space Methods. 4) r7!r ieA (1. Home > Journal of the Physical Society of Japan > Volume 52, Number 11 > On Soliton Solutions of the Nonlinear Coupled Klein-Gordon Equation J. 2019 (2019), No. to obtain the solution of nonlinear fractional Klein-Gordon equation. Inspired by the paper of Donninger-Schlag on this equation, we further investigate the blow up and scattering behavior of its solutions. Signal Processing, 91, 446-451. 2 þ u2 ¼ 0, t Z0, uðx,0Þ ¼ 1 þ sinðxÞ: ð19Þ @t a @x We construct a Homotopy substituting (a = 0, b= 1 and Example 3. 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. 7 (1983), no. Methods Appl. Their combined citations are counted only for the first article. Sterbenz, Global Stability for Charged Scalar Fields on Minkowski. Gepreel and Mohamed S. For a memory function of the type i1+ ( ) where 0 < <1 we derive a fractional Schr odinger-Klein-Gordon equation whose corresponding. of the nonlinear Klein-Gordon equation (1. In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. com Abstract: This paper presents the formulation of time-fractional Klein-Gordon equation using the Euler-Lagrange. Abstract In this paper we study small amplitude solutions of nonlinear Klein Gordon equations with a potential. Analytical approximate solution for nonlinear space-time fractional Klein Gordon equation Khaled A. 5) where eis the electric charge. As a result, iterative method need not be. Feng and A. In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. Sunagawa, Remarks on the asymptotic behavior of the cubic nonlinear Klein-Gordon equations in one space dimension, Differential Integral Equations, 18 (2005), 481-494. 73 (2005), no. 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. Asad Freihat. 2, 345{35 27. So er, Scattering and small data completeness for the critical nonlinear Schr odinger equation. (2017) Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations. On the basis of our solutions we discuss various nonhomogeneous patterns, which can be formed at the critical point of systems described by the Ginzburg–Landau model. We show that Auxiliary equation method provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. A Novel Method to Solve Nonlinear Klein-Gordon Equation Arising in Quantum Field Theory Based on Bessel Functions and Jacobian Free Newton-Krylov Sub-Space Methods. 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. @2w @t2 = @2w @x2 + f(w). The Legendre collocation method is used to reduce. The fractional derivatives are described in the Caputo sense. In this work we study the decay properties of the semilinear Klein-Gordon equation with nonlinearity of fractional order. We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. Conclusions of this paper are summarized in Sect. I: Variants of the phi-four model and the form-I of the nonlinear Klein–Gordon equation Ascensión Hernández Encinas a, Jesus Martín-Vaquero , Araceli Queiruga-Dios ,. Our analysis is based on Aubry's band theory and perturbation theory. Nonlinear Klein-Gordon Equation Necat Polata, Hatice Taskesenb aDepartment of Mathematics, Dicle University, 21280, Diyarbakir bDepartment of Statistics, Yuzuncu Yil University, 65080, Van Abstract. A system of coupled Klein-Gordon equations is suggested to model onedimensional nonlinear wave processes in a bi-layer. Stability and convergence are analyzed using the matrix form of the scheme. 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= , (). of the nonlinear Klein-Gordon equation (1. fractional coupled Klein-Gordon-Schrdinger equations, which does not require a small parameter inthe equations. 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. The time-fractional coupled Klein-Gordon Schrodinger equation is obtained from the coupled Klein-Gordon Schrodinger equation by replacing the order time derivative with a fractional derivative of order α∈(1,2],β∈(0,1]. , Stable solutions of the logarithmic Schrödinger equation, Nonlinear Anal. Sections 5 and 6 are devoted to describe the negative frac-tional probability density situation and the physically acceptable conditions. The nonlinear Klein-Gordon equation is Utt - v2u + pu = f(lu12u). wave equation (where the relevant nonlinear object is the stationary function W whichsolves 1+4W+ W =(d 2) = 0). This work concerns the time averaging techniques for the nonlinear Klein-Gordon (KG) equation in the nonrelativistic limit regime which have recently gained a lot attention in numerical analysis. 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). Under suitable assumption on the potential, we establish the existence and uniqueness of the ground state solution. for a "cosmic superfluid". Mikael Mortensen (mikaem at math. Fractional Klein Gordon Equation ABSTRACT In the present manuscript, a new numerical scheme is presented for solving the time fractional nonlinear Klein-Gordon equation. 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. UNSTABLE GROUND STATE OF NONLINEAR KLEIN-GORDON EQUATIONS BY JALAL SHATAH Abstract. 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. By this method noise terms disappear in the iteration process and single iteration gives the exact solution. (2017) Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations. Hylomorphic solitons in the nonlinear Klein-Gordon equation J. Mohammadi and Hosseini  had showed a new Legendre wavelet operational matrix of derivative in solving singular ordinary differential equations. Strategy: 1 Find a solution of the fractional Klein{Gordon equation that generalizes the fundamental solution of the classical Klein{Gordon equation. We propose and analyze a multiscale time integrator Fourier pseudospectral (MTI-FP) method for solving the Klein--Gordon (KG) equation with a dimensionless parameter $0<\varepsilon\leq1$ which is i. The breather-like spherically symmetric solutions show the constancy of the oscillations fast mode frequency and are three-dimensional objects. Recently published articles from Nonlinear Analysis. (2017) A linearized, decoupled, and energy-preserving compact finite difference scheme for the coupled nonlinear Schrödinger equations. In this study, nonlinear time-fractional Klein-Gordon equations have been analyzed He's variational iteration method. It is second-order in space and time and manifestly Lorentz-covariant. nonlinear Klein-Gordon equation. The local energy also decays. In the Appendices Nonlinear Klein Gordon equations with solitary (travelling) wave solutions are reviewed and solved for particular cases. The residual power series method for solving fractional Klein-Gordon equation Zeliha *Körpınar ABSTRACT In this article, the residual power series method (RPSM) for solving fractional Klein-Gordon equations is introduced. Analysis, 17, (2018), no 4, 1371-1385. KHALID 1, M. Sections 7-10 are devoted for. The solutions are related to soliton solutions of the sine-Gordon equation. 3 Numerical treatment of coupled nonlinear hyperbolic Klein-Gordon equations 249 Legendre, Chebyshev and Gegenbauer polynomials [44–46]. As a result, iterative method need not be employed. Stefanov, Communications in Pure and Appl. 73 (2005), no. Muhammet Kurulay In this paper, the homotopy analysis method is applied to obtain the solution of nonlinear fractional partial differential equations. (2011)) introduced a new approximate formula of the fractional derivative and used it to solve numerically the fractional diffusion equation. The nonlinear Klein-Gordon equation has then become a popular super uid model, which is able to cover the entire velocity range, especially the relativistic region [28, 55, 31, 39, 53, 54, 15, 48, 23, 49, 21, 52]. Introduction Roughly speaking a solitary wave is a solution of a ﬁeld equation whose energy travels as a localised packet and which preserves this localisation in time. and Satbir Malhi. Browse other questions tagged homework-and-exercises lagrangian-formalism conservation-laws noethers-theorem klein-gordon-equation or ask your own question. 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. Ai-Min Yang, Yu-Zhu Zhang, Carlo Cattani, Gong-Nan Xie, Mohammad Mehdi Rashidi, Yi-Jun Zhou, and Xiao-Jun Yang. In paper ]8[ the nonlinear one-dimensional Klein-Gordon equation was solved with the help of the. Fractional Klein-Gordon-Schrödinger Equations with a High-Degree Yukawa Interaction Junjie Wang1,2, Aiguo Xiao1,∗ and Chenxi Wang1 1School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, China. , Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method, Advances in Difference Equations, 2012. For the defocusing nonlinear Schr odinger equation, the semiclassical limit for initial data with Sobolev regularity in short time has been studied by Gre-nier . of the nonlinear Klein-Gordon equation (1. Abstract In this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. In this work we study the decay properties of the semilinear Klein-Gordon equation with nonlinearity of fractional order. least energy steady-state solution of nonlinear Klein-Gordon equations with space dimension n » 3. Wavelet analysis is a recently developed mathematical tool in applied mathematics. 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. A non-local version of these equations are properly described by the fractional version of them. 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. We consider the problem of scattering for the long range critical nonlinear Klein-Gordon in one space dimension. Japan, 58 (2006), 379-400. methods for solving nonlinear fractional Klein-Gordon equation. Some results on the nonlinear Klein-Gordon-Maxwell equations Alessio Pomponio Dipartimento di Matematica, Politecnico di Bari, Italy Granada, Spain, 2011. The case of Maxwell-Schrödinger type coupled equations is also considered. Under suitable assumption on the potential, we establish the existence and uniqueness of the ground state solution. 2, 274-290 Efﬁcient high-order ﬁnite difference methods for nonlinear Klein-Gordon equations. QUAN-FANG WANG. Shu  and the author . The fractional derivatives are deﬁned in the term of Jumarie's operator. Asad Freihat. for a "cosmic superfluid". Four examples are provided to show the accuracy and coherence of the proposed technique. We present an approximate formula of the fractional derivative. 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. The general framework is a nonlinear Klein-Gordon equation in curved spacetime for a complex scalar field, whose phase dynamics gives rise to superfluidity. (Khader et al. Sterbenz, Global Stability for Charged Scalar Fields on Minkowski. 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. Some results on the nonlinear Klein-Gordon-Maxwell equations Alessio Pomponio Dipartimento di Matematica, Politecnico di Bari, Italy Granada, Spain, 2011. nomials for solving the non-linear Fractional (Caputo sense) Klein-Gordon Equation (FKGE). No complete scattering theory has to this day been developed for such equations ; the required Strichartz estimates are still. Introducing a new constraint minimization problem, we prove the existence of ground states for an associated stationary elliptic system. Comparing the methodology with some other known techniques shows that the present approach. This paper is a detailed and self-contained study of the stability properties of periodic traveling wave solutions of the nonlinear Klein-Gordon. 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. Inspired by the paper of Donninger-Schlag on this equation, we further investigate the blow up and scattering behavior of its solutions. 1, 2 Index Terms-- the space-time fractional foam drainage equation; space-time fractional Klein Gordon equation; the modified Kudryashov method. Equations & Applications Volume 3, Number 4 (2011), 527-553 INTERNAL DEGREES OF FREEDOM IN PERTURBED NONLINEAR KLEIN-GORDON EQUATIONS L. Abstract In this paper we study small amplitude solutions of nonlinear Klein Gordon equations with a potential. The KGEs are fundamental class of nonlinear evolution equations arising in classical relativistic and quantum mechanics. Sun, "The improved fractional sub-equation method and its. We show that Auxiliary equation method provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. In this paper, we study a nonlinear Klein-Gordon equation coupled with a Maxwell equation. The Legendre collocation method is used to reduce. 1, 2013, 010201-6. It is second-order in space and time and manifestly Lorentz-covariant. Mikael Mortensen (mikaem at math. nonlinear Klein-Gordon equation with Dirichlet boundary condi-tion on a bounded domain, which shows the overﬂow solution as expected. We study the asymptotic behavior of the semilinear Klein-Gordon equation with nonlinearity of fractional order. 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. Diﬀerential equations involving fractional order derivatives are used to model a variety of systems, of which the im-. The Legendre collocation method is used to reduce. Featured on Meta Feedback post: Moderator review and reinstatement processes. The coupled nonlinear KG types equation will be collocated only for the space vari-. Stability and convergence are analyzed using the matrix form of the scheme. This paper is divided in two parts. SPECTRAL AND MODULATIONAL STABILITY OF PERIODIC WAVETRAINS FOR THE NONLINEAR KLEIN-GORDON EQUATION CHRISTOPHER K. 3) because of its analogue to the nonlinear Schr odinger equation (1. In this paper, we want to understand the dynamics of large, quantized energy. In the compact case, we establish existence of traveling wave solutions via energy minimization methods and prove that at least compact isotropic manifolds have genuinely traveling waves. 1993 Dec;48(6):4768-4778. 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. Sunagawa, Remarks on the asymptotic behavior of the cubic nonlinear Klein-Gordon equations in one space dimension, Differential Integral Equations, 18 (2005), 481-494. [2, 59, 50]. Sections 7–10 are devoted for.  Hossam A. 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. Eman Abuteen. A new numerical algorithm for fractional Fitzhugh–Nagumo equation arising in transmission of nerve impulses D Kumar, J Singh, D Baleanu Nonlinear Dynamics 91 (1), 307-317 , 2018. Sunagawa, Remarks on the asymptotic behavior of the cubic nonlinear Klein–Gordon equations in one space dimension, Differential Integral Equations, 18 (2005), 481–494. 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. 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). v7 Uk 3Q Tx 5T BI Bu y7 BE zu x9 N2 Eq Vo Zg 00 Yz QV M6 Cj 5f 2h 9c 9M sL 5J wD JR qp Tl Zi l8 jJ mc 64 0B uK Vo ya 2R xr rI qY UG vB GZ hy o3 i7 T1 S4 VI 0D An Yv. (2011) On Wave Nonlinear Fractional Klein-Gordon Equation. 2, 274–290 Efﬁcient high-order ﬁnite difference methods for nonlinear Klein–Gordon equations. 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. Muhammet Kurulay in  solve the fractional nonlinear Klein-Gordon equation by means of the homo- topy analysis method. Browse other questions tagged homework-and-exercises lagrangian-formalism conservation-laws noethers-theorem klein-gordon-equation or ask your own question. 19 · DOI : 10. The model under consideration generalizes various nonlinear wave equations, including the sine-Gordon and the nonlinear Klein-Gordon models. We prove that the non-radial sign-cha. The approximate analytical solution of the equation is calculated in the form of a series with easily computable components. Randomized exponential integrator for modulated nonlinear Schrödinger equations (preprint 2018) K. It is second-order in space and time and manifestly Lorentz-covariant. From this end idea we introduce in this paper the concept of generalized. Analytical approximate solution for nonlinear space-time fractional Klein-Gordon equation Khaled A. 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. 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. This paper is divided in two parts. We present an approximate formula of the fractional derivative. Stability and convergence are analyzed using the matrix form of the scheme. As a result, iterative method need not be. fractional-order Klein-Gordon and Gas Dynamics equations. The Klein-Gordon equation plays an important role in mathematical physics. Mohammadi and Hosseini  had showed a new Legendre wavelet operational matrix of derivative in solving singular ordinary differential equations. The method has been successively provided for finding approximate analytica Authors: Muhammet Kurulay. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions. Lindblad and J. Some results on the nonlinear Klein-Gordon-Maxwell equations Alessio Pomponio Dipartimento di Matematica, Politecnico di Bari, Italy Granada, Spain, 2011. Asad Freihat. time-fractional order linear and nonlinear Klein–Gordon equations. Consider fractional nonlinear Klein–Gordon differential equation In Fig. The fractional derivative is considered in the Caputo sense. In the Appendices Nonlinear Klein Gordon equations with solitary (travelling) wave solutions are reviewed and solved for particular cases. It is observed that suggested scheme is highly reliable and may be extended to other nonlinear differential equa-tions of fractional order. of the modulated defocusing nonlinear Klein‐Gordon equation is the defocus‐ ing nonlinear Schrödinger equations. Firstly, we use fractional traveling wave transformations to convert fractional nonlinear partial differential equations to nonlinear ordinary differential equations. On nonlinear fractional Klein-Gordon equation, Signal Processing, 91: 446-451, 2011. construct generalized solitary wave solutions of the nonlinear Klein-Gordon equations of fractional-order. The most downloaded articles from Applied Numerical Mathematics in the last 90 days. for a "cosmic superfluid". Our operational method does not use any integral transforms nor integration processes. Bonanno, and E. Note: Citations are based on reference standards. 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). Discreteness effects on the formation and propagation of breathers in nonlinear Klein-Gordon equations. SULTANA , F. Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method. We study the asymptotic behavior of the semilinear Klein-Gordon equation with nonlinearity of fractional order. Discrete & Continuous Dynamical Systems - A , 2020, 40 (1) : 597-608. 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. A high-order compact scheme for the nonlinear fractional Klein–Gordon equation. We present an approximate formula of the fractional derivative. 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). Thus, the main purpose of this paper is to present the rst step towards a general theory. On the other hand, solving differential equation with fractional derivative might be much. 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 result, new exact travelling wave solutions are obtained. We study the nonrelativistic, semiclassical and nonrelativistic- semiclassical limits of the (modulated) nonlinear Klein-Gordon equations from its hydrodynamical structure via WKB analysis. On space-time means for solutions of nonlinear Klein-Gordon equations Doctoral thesis, 2003. A non-local version of these equations are properly described by the fractional version of them. 2 þ u2 ¼ 0, t Z0, uðx,0Þ ¼ 1 þ sinðxÞ: ð19Þ @t a @x We construct a Homotopy substituting (a = 0, b= 1 and Example 3. Periodic solution of the cubic nonlinear Klein–Gordon equation and the stability criteria via the He-multiple-scales method Published on Jan 1, 2019 in Pramana SCI(E) 1. Eman Abuteen. Then we presented an algorithm of the homotopy perturbation transform method to solve coupled Klein-Gordon-Schrdinger equations. I: Variants of the phi-four model and the form-I of the nonlinear Klein–Gordon equation Ascensión Hernández Encinas a, Jesus Martín-Vaquero , Araceli Queiruga-Dios ,. In this paper, a high order finite difference scheme for a two dimensional nonlinear fractional Klein-Gordon equation in polar coordinates is proposed. A discussion of these results within the framework of linear dispersive wave equations is provided.