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Your hamiltonian density is fine, and for a stationary solution it is just the Bogomol'nyi trick, The sine-Gordon equation (SGE) has applications to Josephson junctions, crystal dislocations, ultra-short optical pulses, relativistic field theory, and elementary Downloadable (with restrictions)! The hierarchy of the sine-Gordon equation with self-consistent sources is derived by using the eigenfunctions of recursion Sine-Gordon Equation in (1+2) and (1+3) dimensions: Existence and Classification of Traveling-Wave Solutions. 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 solution

The time-dependent kink solutions were then found by Lorentz transformation of the time-independent solutions. Interesting quantities such as the kink mass, the charge and the energy density is computed in both phi^4- and the sine-Gordon theory. 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. 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]. Case(2) c0 = c2 2 4c4: In this case, we have k = ¡2.

“solitary waves,” one moving to the left 2009-04-01 Ding, D.-J., et al.: Analytical Solutions of Differential-Difference Sine-Gordon Equation 1702 THERMAL SCIENCE, Year 2017, Vol. 21, No. 4, pp. 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]: soliton solution of such a sine-Gordon model of DNA. Key Words: soliton solution, sine-Gordon, DNA, graphic.

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This is a plot of how the kink-solition solution of the Sine-Gordon equation evolves in time. The data was produced with a semidiscrete solver based on regul The large-time asymptotic solution of the Sine-Gordon equation is considered describing the decay of a step-like initial condition with nonidentical finite-gap limits as x→±∞. The leading term of asymptotics is found as a finite-gap quasi periodic solution with its phase vectors modulated by a slow space-like variable.

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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.

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References Steuerwald, R., Uber enneper’sche Fl¨ achen und B¨ ¨acklund’sche Transformation, Abh. Bayer. Akad.

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A localized structure is an image of the junctions at … The sine-Gordon Equation on a Finite Interval 519 We are interested in the large time asymptotic behavior of the solution of such prob-lems, and in understanding the generation of … The sine-Gordon equation has the following 1-soliton solutions: φ soliton ( x , t ) := 4 arctan ⁡ ( e m γ ( x − v t ) + δ ) {\displaystyle \varphi _{\text{soliton}}(x,t):=4\arctan \left(e^{m\gamma (x-vt)+\delta }\right)\,} 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 into the Sine-Gordon equation (1) then gives 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. The sine-Gordon equation is the classical wave equation with a nonlinear sine source term.

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The method proposed aris. We find the parameters of the transformations corresponding to the Bianchi diagram for the wobble as a particular 3-soliton solutions. We show that this solution 14 Jul 2012 The Sine-Gordon Equation and Solitons - SixtySec Korteweg–de Vries (KdV) equation - Soliton solution as Poschl-Teller potential. 1-soliton solutions[edit]. The sine-Gordon equation has the following 1-soliton solutions:.

Solitary waves: kinks, solitons, and breathers.