Related papers: The sine-Gordon equation on time scales
In this paper it is shown that an equivalent to the complex Klein-Gordon equation can be obtained from the (2+3) dimensional Einstein equations coupled to a conserved energy momentum tensor. In an explicit toy model we give matching…
We discuss the relationship between two-dimensional (2D) dilaton gravity models and sine-Gordon-like field theories. We show that there is a one-to-one correspondence between the solutions of 2D dilaton gravity and the solutions of a (two…
In this paper, we examine the complex sine-Gordon model in the presence of a boundary, and derive boundary conditions that preserve integrability. We present soliton and breather solutions, investigate the scattering of particles and…
We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of nonlinear discrete dispersive equations. Our approach relies…
This paper presents the perturbation theory for the double--sine--Gordon equation. We received the system of differential equations that shows the soliton parameters modification under perturbation's influence. In particular case…
In this paper, we give a formulation of the variational iteration method that makes it suitable for the analysis of the solutions of Klein-Gordon equations with variable coefficients. We particularly study a Klein-Gordon problem which has…
In this report, the various 1D single soliton and multi-soliton solutions of the Sine-Gordon equation are explored. First the topological kink solitons and their properties for the Sine-Gordon, as well as the $\phi^{4}$ model are…
By studying the {\it internal} Riemannian geometry of the surfaces of constant negative scalar curvature, we obtain a natural map between the Liouville, and the sine-Gordon equations. First, considering isometric immersions into the…
In this paper, we propose a reproducing kernel Hilbert space method (RKHSM) for solving the sine--Gordon (SG) equation with initial and boundary conditions based on the reproducing kernel theory. Its exact solution is represented in the…
We investigate the classical and nonclassical reductions of the $2+1$-dimensional sine-Gordon system of Konopelchenko and Rogers, which is a strong generalisation of the sine-Gordon equation. A family of solutions obtained as a nonclassical…
In this article we prove that 2-soliton solutions of the sine-Gordon equation (SG) are orbitally stable in the natural energy space of the problem. The solutions that we study are the {\it 2-kink, kink-antikink and breather} of SG. In order…
We construct a Darboux transformation of a general $su(3)$-valued spin system called the $\Gamma$-spin system. Using this Darboux transformation we derive a recursive formula for the soliton solutions of this spin system. Then using these…
The generalized sine-Gordon (sG) equation was derived as an integrable generalization of the sG equation. In this paper, we develop a direct method for solving the generalized sG equation without recourse to the inverse scattering method.…
By using B\"acklund transformation for the sine-Gordon equation, new periodic exact solutions of the constant astigmatism equation $ z_{yy} + ({1}/{z})_{xx} + 2 = 0 $ are generated from a seed which corresponds to Lipschitz surfaces of…
We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the "equations of motion" on the defect point via the space-like and time-like description. We then exploit the structural…
We obtain the exact nontopological soliton lattice solutions of the Associated Lam\'e equation in different parameter regimes and compute the corresponding energy for each of these solutions. We show that in specific limits these solutions…
Exponentially localized solutions of the Klein-Gordon equation for two and three space variables are presented. The solutions depend on four free parameters. For some relations between the parameters, the solutions describe wave packets…
Positive energy singularities induced by Sine-Gordon solitons in 1+1 dimensional dilaton gravity with positive and negative cosmological constant are considered. When the cosmological constant is positive, the singularities combine a white…
We study the computational complexity of the eigenvalue problem for the Klein-Gordon equation in the framework of the Solvability Complexity Index Hierarchy. We prove that the eigenvalue of the Klein-Gordon equation with linearly decaying…
We give a noncommutative extension of sinh-Gordon equation. We generalize a linear system and Lax representation of the sinh-Gordon equation in noncommutative space. This generalization gives a noncommutative version of the sinh-Gordon…