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1701-1705 In this paper, we extend the Jacobian elliptic function method [15] to a variable co-efficient method, and use this method to solve the discrete sine-Gordon equation [14, 16]: 1 1 dd sin( ) dd Sine-Gordon Expansion Method for Exact Solutions to Conformable Time Fractional Equations in RLW-Class Alper Korkmaza;, Ozlem Ersoy Hepsonb, Kamyar Hosseinic, Hadi Rezazadehd, Mostafa Eslamie We obtain exact solutions U(x, y, z, t) of the three-dimensional sine-Gordon equation in a form that Lamb previously proposed for integrating the two-dimensional sine-Gordon equation. The three-dimensional solutions depend on arbitrary functions F(α) and ϕ(α,β), whose arguments are some functions α(x, y, z, t) and β(x, y, z, t). The ansatzes must satisfy certain equations. These are an In this scheme we advance the solution of the (2+1) sine-Gordon partial differential Equation (1) from nth plane to (n+1)th plane by replacing u xx by implicit finite difference approximation at the (n+1)th plane. Similarly, u tt, u yy and u t are replaced by an explicit central finite difference approximation at the nth plane as in equations the SINE-GORDON Equation in To understand quantitatively how soli-tons can result from a delicate balance of dispersion and nonlinearity, let us be-gin with the linear, dispersionless,bi- directional wave equation By direct substitution into Eq. 1, it is is a solution for any functions f and g.

Sine gordon solution

Akad. Wiss. (Muench.), Vol. 40, pp. 1–105, 1936. Gordon equation, multiple-soliton solutions.

Fourth order accurate numerical solution of the - UPPSATSER.SE

INTRODUCTION. The sine-Gordon equation (SGE) has been studied exhaustively with well-known soliton solutions. In. 2 + 1 dimensions, the SGE has many 11 Feb 2020 equations with symmetries and kink wave solutions.

Jonatan Lenells: Asymptotics for the sine-Gordon equation in

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Bjorn lindblom

The global kernel method resulted the dense differentiation matrices and hence difficult to apply for problem with large amount of data points. The present numerical scheme is local with sparse differentiation matrices, consequently capable of removing the deficiency of ill- One-dimensional solitary wave solutions with soliton properties are well known from problems in many branches of physics. Soliton solutions have been found in a variety of nonlinear differential equations such as the Korteweg and deVries equation, the Schrödinger equation, the sine-Gordon (SG) equation, etc.

A positive 1-soliton solution to the Sine–Gordon equation. Xerox Services includes a continuum of solutions and services that helps Nicholas Graziano, Cheryl Gordon Krongard, Scott Letier and Sara Martinez Tucker.
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A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable x and the tempo Many researchers have proposed different solutions for sine-Gordon equation. Wazwaz presents several solutions for a special generalized sine-Gordon equation by using the tanh method which introduces a variable with tanh form to transform the original PDE equation into an ODE [18, 19].