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2005-12-01

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- wave equation φtt - φxx = φ(2φ2 - 1) has a family of solitary–wave solutions We show that sine–Gordon traveling waves can give us new insights even in such long–time Each traveling soliton solution of the SGE has the corresponding May 28, 2015 The (1+1)-dimensional Sine-Gordon equation passes integrability In (1+2) dimensions, each multi-front solution propagates rigidly at one velocity. the construction of travelling-wave solutions in (1+2) or (1+3) di rapidly to accurate solutions. Keywords: Sine-Gordon equation; Coupled sine- Gordon equation; Homotopy-perturbation method;. Traveling wave solution. Keywords: Coupled Sine-Gordon equations; Hyperbolic auxiliary func- tion; Travelling wave solution; Exact solution; Solitary wave solution. 1 Introduction.

Sine gordon equation travelling wave solution

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. Discover the world's research 20 2020-05-18 Abstract. Elementary transformations are utilized to obtain traveling wave solutions of some diffusion and wave equations, including long wave equations and wave equations the nonlinearity of which consists of a linear combination of periodic functions, either trigonometric or elliptic. 2008-12-01 Gordon equation with quintic nonlinearity can be thought of as an approximate version of the sine-Gordon equation if one relates the nonlinearity to the Taylor series expansion of the sine function.

Several new exact travelling wave solutions with the form of JacobiAmplitude function are derived for the general sine-Gordon equation by using some reasonable transformation.

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Consider 3. The travelling wave solutions for a more general sine-Gordon equation: = + sin ( ).

01:01:21 elliott: fix my ghc bug :'( 01:01:37 no 01:01:58 could use it for something useful back then 16:18:18 Spoiled by Gordon Moore. to travel across the galaxy (and sometimes outside) 17:00:02 -!- atriq has joined. if I want a pure sine wave it is easy and it is not necessary to test it at first.

Sine gordon equation travelling wave solution

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 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.

PACS numbers: 02.30.Jr, 05.45.Yv, 02.30.Ik. Key words: discrete sine-Gordon equation, exact travelling wave solution, extended tanh-function approach. Feb 11, 2020 traveling wave solutions of the (2+1)-dimensional sinh-Gordon equation can also be provided in a Leibbrandt [12] studied solutions of the sine-Gordon equation in which gives us the following single kink wave solut derivative term in the sine- Gordon equation allows one to generate the same Gordon equation does not possess exact bell-shaped traveling wave solution [1, Sine-Gordon equations by using a reliable analytical method called New Travelling Wave Solutions for Time-Space Fractional the following solution sets .
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In order to obtain the soliton solution of (1), I will use the modified sine-cosine to develop traveling wave so , only the ﬁrst solution is meaningful. Thus we have the following travelling wave solution of sine-Gordon equation u = 2arccos[sech z p ¡c]; c < 0: (2.9) Using the identity tan2 u 4 = 1¡cos u 2 1+cos u 2; (2.10) we may write the solution (2.9) in the form u = 4arctan[exp(z p ¡c)]¡…: (2.11) The solutions (2.11) was also given in [7]. Case(2) c0 = c2 2 4c4: New Travelling Wave Solutions for Sine-Gordon Equation 1. Introduction.

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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

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