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Keywords: Coupled Sine-Gordon equations; Hyperbolic auxiliary func- tion; Travelling wave solution; Exact solution; Solitary wave solution. 1 Introduction.

Comput. 215 (2009). 3777-3781 ] are analyzed. We have observed that fourteen solutions by Li from thirty do not satisfy the equation.

Sine gordon equation travelling wave solution

Double Sine–Gordon equation JacobiAmplitude Traveling wave solution Implicit solution abstract Under the assumption that u0 is a function form of einu, this paper presents a new set of traveling-wave solutions with JacobiAmplitude function for the generalized form of the double Sine–Gordon equation u tt ¼ ku xx þ2asinðnuÞþbsinð2nuÞ 2015-05-28 · Although the Sine-Gordon equation was derived for quite a few physical systems that have nothing to do with Special Relativity, the equation itself emerges as a non-linear relativistic wave equation. This is why in later years it has found applications in theoretical High-Energy Physics (e.g., in Relativistic Quantum Field Theory, and, in recent years, in String Theory). Exact solutions of the Nizhnik-Novikov-Veselov equation by Li [New kink-shaped solutions and periodic wave solutions for the (2+1)-dimensional Sine-Gordon equation, Appl. Math.

Traveling-wave solutions: w(x,t) = 4 ‚ arctan ‰ exp • ± b‚(kx+„t obtaining traveling wave solutions of nonlinear partial diﬀerential equa-tions. Applying this, exact traveling wave solutions for the coupled Sine-Gordon equations are constructed. Mathematics Subject Classiﬁcation: 35Q58; 37K50 Keywords: Coupled Sine-Gordon equations; Hyperbolic auxiliary func- 2007-07-01 As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach.

Traveling Wave Solutions of the Sine-Gordon and the Coupled Sine-Gordon Equations Using the Homotopy-Perturbation Method A. Sadighi1, D.D. Ganji1; and B. Ganjavi2 Abstract. In this research, the Homotopy-Perturbation Method (HPM) has been used for solving sine-Gordon and coupled sine-Gordon equations, which have a wide range of applications in physics.

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Introduction. In recent years, nonlinear It is denominated following its similar form to the Klein-Gordon equation.

The 2-soliton solutions of the sine-Gordon equation show some of the characteristic features of the solitons. The traveling sine-Gordon kinks and/or antikinks pass through each other as if perfectly permeable, and the only observed effect is a phase shift. The spectrum of travelling wave solutions to the Sine-Gordon equation.
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When c2 − 1 > 0 they are called superluminal waves. We have the following theorem: Theorem 1. Kink wave solutions to equation (1) utt = uxx + sin u, are spectrally stable if c2 6= 1. 2.1.
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We construct a new Evans function for quasi-periodic solutions to the linearisation of the sine-Gordon equation about a periodic travelling wave. This Evans function is written in terms of fundamental solutions to a Hill’s equation.

On kinks and other travelling-wave solutions of a modi ed sine-Gordon equation Gaetano Fiore 1;2, Gabriele Guerriero , Alfonso Maio , Enrico Mazziotti 1Dip. di Matematica e Applicazioni, Universit a \Federico II", V. Claudio 21, 80125 Napoli 2I.N.F.N., Sezione di Napoli, Complesso MSA, V. Cintia, 80126 Napoli email: gaetano. ore@unina.it Abstract The 2-soliton solutions of the sine-Gordon equation show some of the characteristic features of the solitons. The traveling sine-Gordon kinks and/or antikinks pass through each other as if perfectly permeable, and the only observed effect is a phase shift. Travelling wave solutions of the sine-Gordon equation are written in the form u(x, t) = f(x − ct), where c is the wave speed and f (x): R → R is the wave profile satisfying the following differential equation: Using the methods of dynamical systems for the (n + 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions Under the assumption that u ′ is a function form of e inu, this paper presents a new set of traveling-wave solutions with JacobiAmplitude function for the generalized form of the double Sine–Gordon equation u tt = ku xx + 2 α sin (nu) + β sin (2 nu).