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The (+) branch of the kink-type solitary wave solution (25) at time in the form of traveling wave φ(x,t)=U(θ), θ=x−c0t. Then the sine-Gordon equation will take the form (c02−1)Uθθ+sinU=0. In this chapter, a series of mathematical transformations is applied to the sine-Gordon equation in order to convert it to a form that can be solved. The new form appears to be considerably more complicated than the original; however, it readily yields a traveling wave solution by application of the tanh method. 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.
using the method which arises from a two-step, one parameter method for the numerical solution of second-order ordinary differential equations . All these profound results are pretty beautiful and important not only in mathematics, but The spectrum of travelling wave solutions to the Sine-Gordon equation. Discrete & Continuous Dynamical Systems - S , 2012, 5 (5) : 925-937. doi: 10.3934/dcdss.2012.5.925 Solutions Traveling wave Let us look for solutions of the sine-Gordon equation φ t t − φ x x = sin φ. in the form of traveling wave φ (x, t) = U (θ), θ = x − c 0 t.
Keywords: (G'/G)-expansion method, Traveling wave solution, Sine-Gordon equation, Sinh-Gordon equation, Liouville equation.
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Ricatti equations and further geometric considerations are also used in establishing stability. Sine-Gordon Equation The sine-Gordon equation is a nonlinear hyperbolic partialdifferential equation in-volving the d’Alembert operator and the sine of the unknown function. The equa-tion, as well as several solution techniques, were known in the nineteenth century in the course of study of various problems of differential geometry. The equation
2020-04-01 · Lie symmetries analysis and traveling wave solutions of the (2+1)-dimensional sine-Gordon equation Obviously, the following simple transformation (55) v = e i u , sends (56) sin u = v − v − 1 2 i , cos u = v + v − 1 2 , and (57) u = arccos v + v − 1 2 .
In the present work it is Download Citation | New Exact Travelling Wave Solutions for (2+1) dimensional Sine Gordon and Kadomtsev Petviashvili Equations | In this paper, by using the solutions of an auxiliary ordinary 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.
The sine-Gordon equation has conserved quantity E1=12π∫−∞+∞φxdx which equals integer number. This conservation law is called topological chargeof solution φ(x,t).
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Key words: discrete sine-Gordon equation, exact travelling wave solution, extended tanh-function approach.
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II The sine-Gordon Equation ] also presents some exact travelling wave solutions for a more general sine-Gordon equation: In this paper, a method will be employed to derive a set of exact travelling wave solutions with a JacobiAmplitude function form which has been employed to the Dodd-Bullough equation and some new travelling wave solutions have been derived [ 22 And [ ]alsopresentssomeexact travelling wave solutions for a more general sine-Gordon equation: = + sin ( ). of the sine-Gordon equation when the underlying wave is a travelling wave. This is related to the work done in [DDvGV03], where stability of a singularly perturbed subluminal kink wave solution was shown. Travelling wave solutions to the sine-Gordon equation for which the quantity c2 1 < 0 are called subluminal waves. 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.
2017-11-01 Kink Waves Travelling wave solutions to the sine-Gordon equation for which the quantity c2 − 1 < 0 are called subluminal waves. When c2 − 1 > 0 they are called superluminal waves. We have the following theorem: Theorem 1. Kink wave solutions to equation (1) utt = uxx + … Request PDF | On Jul 3, 2020, S. P. Joseph published TRAVELING WAVE EXACT SOLUTIONS FOR GENERAL SINE-GORDON EQUATION | Find, read and cite all the research you need on ResearchGate in the form of traveling wave φ(x,t)=U(θ), θ=x−c0t. Then the sine-Gordon equation will take the form (c02−1)Uθθ+sinU=0. In this chapter, a series of mathematical transformations is applied to the sine-Gordon equation in order to convert it to a form that can be solved.