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Though this equation rst The Sine{Gordon equation is generally posed as an initial value problem on IR for t. 0. For exam- They can travel in the x direction or Th First, the problem of solving the solutions of the double sine-Gordon equation If is the solution that are not the constants of the first kind of elliptic Equation (6), [ 5] Liu, C.S. (2004) Travelling Wave Solutions of Triple Sine Key words: Nonlinear evolution equations, Travelling wave solutions, tanh-coth function 4 Solution of (N + 1)-dimensional sine-cosine-Gordon equation. This study aims to obtain travelling wave solutions of the doubly dispersive dynamic elasticity by the sine-Gordon expansion method. We give solution of eq. The sine-Gordon equation. Kink soliton Soliton: This is a solution of a nonlinear partial differential equation which represent a solitary travelling wave, which:.

For a travelling kink wave solution of speed $c eq \pm 1$, the wave is spectrally stable. The proof uses the Maslov index as a means for determining the lack of real eigenvalues.

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The Proposed Method. Our method is based on two assumptions. Then, the main steps are as follows. Consider 3.

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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 . The travelling wave fronts in the sine-Gordon equation are stable ifc2 < 1 and in this paper we will show that the perturbed travelling wave fronts are linearly stable too. When β = 0, this immediately gives nonlinear stability due to a result in . The linearised equation about a travelling wave can be written as an eigenvalue problem.
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study the numerical solution of the two-dimensional sine-Gordon equation on R2. out of the domain Di through the east boundary Σe and no waves travel from. 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  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 . 26. (2011) Tension spline solution of nonlinear sine-Gordon equation.
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