The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation.It is second-order in space and time and manifestly Lorentz-covariant.It is a quantized version of the relativistic energy–momentum relation.Its solutions include a quantum scalar or pseudoscalar field, a field whose

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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 We use the tanh method and a variable separated ODE method for solving the double sine-Gordon equation and a generalized form of this equation. 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. Let a 0 , ta , (,]g be a function defined on at and .

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 In this paper, we use the generalized kudryashov method to seek the traveling wave solutions of the 2-dim sine Gordon and the double sine-Gordon and equations. travelling wave solutions for a more general sine-Gordon equation: = + sin ( ). ( ) 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 … 2007-02-01 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. We have found these solutions of the equation in the trigonometric, complex and hyperbolic function forms. solutions to the sine-Gordon equation with a solution u to the We considered traveling wave backgrounds u(˘; ) = f(˘ ), where f : R !R. The wave speed can be set to one because of the Lorentz transformation.

Applying this, exact traveling wave solutions for the coupled Sine-Gordon equations are constructed.

2006-07-01

Keywords: (G'/G)-expansion method, Traveling wave solution, Sine-Gordon equation, Sinh-Gordon equation, Liouville equation. Abstract.

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 …

Sine gordon equation travelling wave solution

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.

wave solution of Eq. (3), considering the homogeneous balance of the two highest nonlinear terms u uxx. Second-Order Hyperbolic Partial Differential Equations > Sine-Gordon Equation. 6. ∂2w Traveling-wave solutions: w(x, t) = 4 The first expression corresponds to a single-soliton solution. 2◦ . Functional separable solutions: w(x Apr 21, 2020 Traveling wave solutions of the sine-Gordon equation are of the form its corresponding solution χ to the Lax equations (3.1) and (3.2) with a Note that (13) confirms to the condition for a double well potential well and there by existence of tanh soliton [9].
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Then the sine-Gordon equation will take the form (c02−1)Uθθ+sin⁡U=0. 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. On kinks and other travelling-wave solutions of a modi ed sine-Gordon equation Gaetano Fiore 1;2, Gabriele Guerriero , Alfonso Maio , Enrico Mazziotti 1Dip.
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The sine-Gordon equation. Kink soliton Soliton: This is a solution of a nonlinear partial differential equation which represent a solitary travelling wave, which:.

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