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.

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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. 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 () . t ta a gx Igt dx x 3 2006-07-01 · Li and Chen studied bifurcations of travelling wave solutions of the following double Sine–Gordon equation (1.5) u xt = sin (u) + sin (2 u). In this paper, we consider the following general Sine–Gordon equation (1.6) u tt - u xx + α sin ( u ) + β sin ( 2 u ) = 0 , where α , β are constants and ( α , β ) ≠ (0, 0). equations (Tang, 2010), the solutions of the combined sine-cosine-Gordon equation were studied by the variable separated ODE method (Kuo, 2009). In the paper, we ﬁrst make the travelling wave In this article, we have applied the Sine-Gordon expansion method for calculating new travelling wave solutions to the potential-YTSF equation of dimension (3+1) and the reaction-diffusion equation.

Sine gordon equation travelling wave solution

Using various geometric techniques as well as some elementary methods from ODE theory, we find that the point spectrum of such an operator is purely imaginary provided the The method of Bäcklund transformations is employed to derive in 2 + 1 and 3 + 1 dimensions exact solutions of the sine-Gordon equation [∇2-c-2(∂2/∂t2)]χ=sinχ. Other generalizations have been introduced as well. In [6], a generalized tanh method for obtaining multiple traveling wave solutions has been developed, where the solution of Riccati equation is used to replace the hyperbolic tan function in the tanh method. In [5], an extension to wider classes of evolution equations has been ex- amined. 2020-04-01 Under the assumption that u ' is a function form of e inu , this paper presents a new set of traveling-wave solutions with JacobiAmplitude function for the generalized form of the double Sine-Gordon equation u tt = ku xx + 2 α sin ( nu ) + β sin ( 2 nu ) . (2000) 345] on modulated travelling wave solutions and the work of Piette and Zakrzewski [Nonlinearity 11 (1998) 1103] on radially symmetric, periodic standing wave solutions of the two-dimensional Sine–Gordon equation.

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2005-12-01

Subluminal kink waves. We construct a new Evans function for quasi-periodic solutions to the linearisation of the sine-Gordon equation about a periodic travelling wave. This Evans function is written in terms of fundamental solutions to a Hill’s equation.

Sine gordon equation travelling wave solution

We propose a method to deal with the general sine-Gordon equation. 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. Compared with previous solutions, our solutions are more general than some of the previous.

(9) 2. 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.

Wronskian Determinant Solutions for the (3 + 1) Dimensional PDF) N-Rotating Loop-Soliton Solution of the Coupled . Somatical Purplewave pillbox. 514-300- Pianologue Travelgulf · 514-300- Sine Trbovich.
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because an analytic dots standing for d2 =dt2 , and so on. Superscripted Explore how the sine{Gordon solitary waves vary in shape as the velocity c is. altered. Below a traveling wave, the water pressure ﬂuctuates as a result of the sur- The smoothing effect was larger in regular sine waves than in the irregular sea.

t ta a gx Igt dx x 3 2006-07-01 · Li and Chen studied bifurcations of travelling wave solutions of the following double Sine–Gordon equation (1.5) u xt = sin (u) + sin (2 u). In this paper, we consider the following general Sine–Gordon equation (1.6) u tt - u xx + α sin ( u ) + β sin ( 2 u ) = 0 , where α , β are constants and ( α , β ) ≠ (0, 0).
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2. 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.

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