Abstract: In this paper, differential transform method (DTM) is applied to the sine-Gordon equation which arise in differential geometry, propagation of magnetic flux, stability of fluid motions, nonlinear physics and applied sciences. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational task. Exact solutions can also be ac...

Algebro-geometric Poisson brackets for real, finite-zone solutions of the Korteweg–de Vries (KdV) equation were studied in [1]. The transfer of this theory to the Toda lattice and the sinh-Gordon equation is more or less obvious. The complex part of the finite-zone theory for the nonlinear Schrödinger equation (NS) and the sine-Gordon equation (SG) is analogous to KdV, but conditions that solut...

The collision between a kink and a high amplitude breather in the Frenkel-Kontorova chain with a small degree of discreteness was studied numerically and the results were compared with an exact three-soliton solution to the sine-Gordon (SG) equation. It was found that there exists a narrow range of parameters of quasiparticles where the collision in the discrete system is strongly inelastic and...

We develop a perturbation theory that describes bound states of solitons localized in a confined area. External forces and influence of inhomogeneities are taken into account as perturbations to exact solutions of the sine-Gordon equation. We have investigated two special cases of fluxon trapped by a microresistor and decay of a breather under dissipation. Also, we have carried out numerical si...

Two sets of super Riccati equations are presented which result in two linear problems of super sine-Gordon equation. The linear problems are then shown to be related to each other by a super gauge transformation and to the super Bäcklund transformation of the equation. PACS: 02.30.Ik PACS: 12.60.Jv On leave of absence from PRD, PINSTECH, Nilore Islamabad (Pakistan).

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 temporal variable t, and they are exponentially asymptotic to integer multiples of 2π as x → ±∞. The solution formulas are expressed explicitly in terms of a real triplet of constant matrices. The method p...

A comprehensive symmetry analysis of the N = 1 supersymmetric sine–Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to the coefficients of the various powers of the anticommuting independent variables. Next, we consider the supersine-Gordon equation expressed in terms of a...

Abstract: Haar wavelet method for solving the Klein–Gordon and the sine-Gordon equations has been implemented. Application to partial differential equations is exemplified by solving the sine-Gordon equation. The efficiency of the method is demonstrated by five numerical examples. Computer simulation is carried out for problems the exact solution of which is known. This allows us to estimate th...

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 reduction involves a decoupled sum of solutions of a generalised, real, pumped Maxwell-Bloch system. This implies the existence of families of solutions, all ...