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 …

Exact, particular solutions of the double sine Gordon equation in n dimen- sional space are constructed. Under certain restrictions these solutions are N solitons

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 For other exact solutions of the sine-Gordon equation, see the nonlinear Klein–Gordon equation with f(w) =bsin(‚w). 5–. The sine-Gordon equation is integrated by the inverse scattering method. References Steuerwald, R., Uber enneper’sche Fl¨ achen und B¨ ¨acklund’sche Transformation, Abh. Bayer. Akad. Wiss.

Sine gordon solution

Different analytical or approximate solutions have been obtained to analyze the physical phenomena.5,9,16 A variety of particular solutions have been discovered by using several transformations.2,1 In particular, the transformation given by ␪共x1,x2兲 = 4 arctan 冋册 F共x1兲 G共x2兲共6兲 allows researchers to derive several classes and types of solutions.1,9–15 In this paper, we present a new analytical solution … The sine-Gordon soliton is identified with the fundamental fermion of the Thirring model. Several topics involving renormalization group ideas are reviewed. The solution of the s-wave Kondo A breather is a localized periodic solution of either continuous media equations or discrete lattice equations. The exactly solvable sine-Gordon equation and the focusing nonlinear Schrödinger equation are examples of one-dimensional partial differential equations that possess breather solutions. Discrete nonlinear Hamiltonian lattices in many cases support breather solutions. Numerical simulation of the solution to the sine-Gordon equation on the whole real axis is considered in this paper.

Sine-Gordon Equation.

2019-11-18

(Muench.), Vol. 40, pp. 1–105, 1936. 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 solution of sine-Gordon equation in circular domain.

mulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable x and the temporal variable t; and they are exponentially asymptotic to integer multiples of 2… as x ! §1: The solution formulas are expressed explicitly in terms of a real triplet of constant matrices.

In Section 3, the sine-Gordon expansion method is implemented to produce the exact traveling wave solutions of the Tzitzeica type equations in nonlinear optics; and finally, a short conclusion is provided in Section 4. 2. formulas for exact solutions to the sine-Gordon equation uxt = sinu; (1.1) where u is real valued and the subscripts denote the partial derivatives with respect to the spatial coordinate x and the temporal coordinate t: Under the transformation x 7!ax + t a; t 7!ax ¡ t a; where a is a positive constant, (1.1) is transformed into the alternate form The sine-Gordon equation is the classical wave equation with a nonlinear sine source term.

2013-03-22 The Sine Gordon Equation In[1]:=Clear@"Global One Soliton Solutions We display a soliton solution; first of all for the special case of no time depen-dence. We verify that the equation is satisfied by giving the command sinegordoneq and seeing that the result is True.
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Spredning - i alle Several different solutions of utilising the power in the three main Sneve M K, Gordon B, Smith G M and Fowell S. Support in Development of.

The ﬁeld of soliton is h = φ x = 2 cosh(√x−ut 1−u2),h| x=0 =2 solution of sine-Gordon equation u = 2arccos[sech z p ¡c]; c < 0: (2.9) Using the identity tan2 u 4 = 1¡cos u 2 1+cos u 2; (2.10) we may write the solution (2.9) in the form u = 4arctan[exp(z p ¡c)]¡…: (2.11) The solutions (2.11) was also given in [7].
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Abstract: We study exact soliton solutions of the Sine-Gordon (SG) equation with variable coefficient. Based on the similarity transformation and Hirota's bilinear.

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.