rapidly to accurate solutions. Keywords: Sine-Gordon equation; Coupled sine- Gordon equation; Homotopy-perturbation method;. Traveling wave solution.

2010-10-13 · Abstract: We give a geometric proof of spectral stability of travelling kink wave solutions to the sine-Gordon equation. 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. Ricatti equations and further geometric considerations are also used in establishing stability.

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Sine gordon equation travelling wave solution

(2). rapidly to accurate solutions. Keywords: Sine-Gordon equation; Coupled sine- Gordon equation; Homotopy-perturbation method;. Traveling wave solution. Nonchiral intermediate long-wave equation and interedge effects in narrow quantum Boundary value problems for the elliptic sine-gordon equation in a of all travelling-wave solutions for some nonlinear dispersive equations2007Ingår i: Traveling wave solutions of the Camassa-Holm equation2005Ingår i: Journal of On a novel integrable generalization of the sine-Gordon equation2010Ingår i: av B Shuaib · 2018 — together with the sine-Gordon equation utt −uxx +sinu = 0 The CH and DP equations have peaked travelling wave solutions (peakons) of the simple form.

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.

Note that (13) confirms to the condition for a double well potential well and there by existence of tanh soliton [9]. Let us look for travelling wave solutions of the sine-

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.

Sine gordon equation travelling wave solution

We can see that this is yx=0 = − A sin ωt, which is the equation for simple harmonic motion, with angular frequency ω = 2πv/λ. Knowing ω we can calculate the

Case(2) c0 = c2 2 4c4: We propose a method to deal with the general sine-Gordon equation.

Introduction. In recent years, nonlinear It is denominated following its similar form to the Klein-Gordon equation. The equation, as well as several solution techniques, was known in the 19th century, but travelling wave moving with velocity c, and that the general solution to the equation utt − c2uxx is the NLS, and Sine-Gordon equation are also CPT- invariant. Keywords: (G'/G)-expansion method, Traveling wave solution, Sine-Gordon equation, Sinh-Gordon equation, Liouville equation.
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Wazwaz [11] used the tanh method to construct traveling wave solutions for the Klein–Gordon equation with quintic nonlinearity. 2005-12-01 For the (n + 1)-dimensional sine- and sinh-Gordon equations, by using the approach of dynamical systems to a class of travelling wave solutions, in 21 different regions of a five-parameter space 2020-06-17 New Doubly Periodic Solutions of (2+1)-Dimensional Nonlinear Wave Equations via the Generalized Sine-Gordon Equation Expansion Method Zhenya Yan∗ Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of … 2.2 Traveling Wave Reduction Traveling wave solutions of the sine-Gordon equation are of the form u(x;t) = f(x ct); (2.3) where cis a real valued constant often refered to as the wave speed and f: R ! R. Substituting (2.3) into (2.1) creates an Ordinary Diﬀerential Equation (ODE) reduction of the sine-Gordon equation … but solving nonlinear equations is still an important task -[27][30].

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av I Nakhimovski · Citerat av 26 — differential equation solver for the numerical solution of the resulting system of equa- tions. This solver is Fourier(φ, j) generates sine and cosine pair for the j-th wave. • nr,r, nr,φ, nr,z, 136, 1990. [21] A. Veitl, T. Gordon, A. Van De Sand, M. Howell, M. Valasek, O. Vaculin, on Travel and Travel Patterns, 2004, ISBN 91-.

Several exact travelling wave solutions are formally For example, the travelling wave solutions of the (1+2)-dimensional Kadomtsev-Petviashvili II equation (KP II) are solitons, and those of the higher-dimensional Sine-Gordon equation are fronts. Still, localized structures, which emulate spatially extended particles, can be generated from such solutions in two or three space dimensions by a procedure that is a natural consequence of the Article. Some New Exact Traveling Wave Solutions of Double-sine-Gordon Equation. February 2008; Communications in Theoretical Physics 49(2):303 New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations 3 1 Definition 2.

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] 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

Let us look for travelling wave solutions of the sine-Gordonequation (5.1) of the form u(ξ):=u(x−ct), 45. 2019-12-01 The sine-Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function. It was originally introduced by Edmond Bour (1862) in the course of study of surfaces of constant negative curvature as the Gauss–Codazzi equation for surfaces of curvature −1 in 3-space, and rediscovered by Frenkel and … 2006-07-01 New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations 3 1 Definition 2. Let a 0 , ta , (,]g be a function defined on at and . Then, 2 the th order fractional integral of function g is defined as (Khalil et al., 2014), 1 () .

Sine-Gordon equations by using a reliable analytical method called New Travelling Wave Solutions for Time-Space Fractional the following solution sets . 26.

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In addition to the known solutions of theses equations, some new solutions will also be given. 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.