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Case(2) c0 = c2 2 4c4: New Travelling Wave Solutions for Sine-Gordon Equation 1. Introduction. The sine-Gordon equation appears in differential geometry and relativistic field theory. It is 2. The Proposed Method. Our method is based on two assumptions. Then, the main steps are as follows.

Sine gordon equation travelling wave solution

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Sine gordon equation travelling wave solution

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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 + sin u, are spectrally stable if c2 6= 1. 2.1. Subluminal kink waves.

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. 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+sin⁡U=0.
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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. We have the following theorem: Theorem 1.

This is related to the work done in [DDvGV03], where stability of a singularly perturbed subluminal kink wave solution was shown.
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Various extension forms of the tanh method have been developed. First a power series in tanh was used as an ansatz to obtain analytical solutions of traveling wave type of certain nonlinear evolution equations.