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Using v = a1` and equation (1.7), we obtain the following solutions v = †tan z p Unperturbed sine-Gordon equation has exact solution: φ(x,t) = 4arctanexp ±√x−ut 1−u2 This is a solitary wave or soliton. It can move with velocity 0 ≤ u<1 (i.e. c¯0!). Picture. Soliton is a kink which changes the Josephson phase from 0 to 2π (soliton) or from 2π to 0 (anti-soliton). The ﬁeld of soliton is h = φ x = 2 cosh(√x−ut 1−u2),h| x=0 =2 Solutions.
The nonlinear sine-Gordon equation (SGE), a type of hyperbolic partial differential equation, is often used to describe and simulate the physical phenomena in a variety of fields of engineering and science, such as nonlinear waves, propagation of fluxons and dislocation of metals [ 1 – 4 ]. means that interchanging space and time variables preserves the solution, as required by the symmetry of the sine-Gordon equation (1). (Although the reason for the factor of 4 is not entirely clear.) Plugging the ansatz ( 16 ) into the Sine-Gordon equation (1) then gives For other exact solutions of the sine-Gordon equation, see the nonlinear Klein–Gordon equation with f(w) =bsin(‚w). 5–.
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I was wondering if anyone knows the steps to determining the sine-gordon solution for a traveling wave. Thanks. you can post here or e-mail me directly at - Exact Solutions to the Sine-Gordon Equation Francesco Demontis (based on a joint work with T. Aktosun and C. van der Mee) University of Cagliari Department of Mathematics and Computer Science IMA Conference on Nonlinearity and Coherent Structures. Reading, July, 6-8 2011.
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solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do … The nonlinear Sine-Gordon equation is one of the widely used partial differential equations that appears in various sciences and engineering.
The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is described, in which the sine-Gordon field is decomposed into slow and fast modes. An effective theory for the slow modes is derived and rescaled to yield the flow equations for the model. The resulting Kosterlitz–Thouless phase diagram is
In this paper, by means of a proper orthogonal decomposition (POD) we mainly reduce the order of the classical Crank–Nicolson finite difference (CCNFD) model for the fractional-order parabolic-type sine-Gordon equations (FOPTSGEs). Toward this end, we will first review the CCNFD model for FOPTSGEs and the theoretical results (such as existence, stabilization, and convergence) of the CCNFD
The Sine Gordon Equation In:=Clear@"Global One Soliton Solutions We display a soliton solution; first of all for the special case of no time depen-
I've attached a mathcad file. I was wondering if anyone knows the steps to determining the sine-gordon solution for a traveling wave.
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It is well known in the commutative case that one may obtain reductions by imposing periodic conditions on the θ n. Similarly in the non-Abelian case, one can make periodic reductions of . From now on, we only … Klein–Gordon equation4,5 in some special cases.
As an example of the application of these solutions, we consider the 2-periodic reduction to a matrix sine-Gordon equation. In particular, we investigate the
5 Feb 2018 tial differential equations; graph theory; sine–Gordon equation. MSC:  Numerical solutions for kinks and breathers on a given graph are.
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For other exact solutions of the sine-Gordon equation, see the nonlinear Klein–Gordon equation with f(w) =bsin(‚w). 5–.
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constant speed) Equation, Soliton, Long Wave length soliton solution. I. INTRODUCTION. Sine Gordon Equation is a partial differential equation which appears in differential As an application, we construct for the matrix sine-Gordon equation N-soliton solutions analogous to the multisoliton solutions for the KdV equation due to This paper develops a local Kriging meshless solution to the nonlinear 2 + 1- dimensional sine-Gordon equation. The meshless shape function is constructed by In this paper we describe stability properties of the Sine-Gordon breather solution . These properties are first described by suitable variational elliptic equations, 1 Jan 2020 Abstract: In this paper authors applied sub-equation method to obtain the new exact solutions of the MkdV-Sine-Gordon equation.