Dynamics of kink-soliton solutions for $2+1$-dimensional sine-Gordon equation
Abstract
In this paper we study the dynamics of explicit solutions of -dimensional (D) sine-Gordon equation. The Darboux transformation is applied to the associated linear eigenvalue problem to construct nontrivial solutions of D sine-Gordon equation in terms of ratios of determinants. We obtained a generalized expression for -fold transformed dynamical variable which enables us to calculate explicit expressions of nontrivial solutions. In order to explore the dynamics of kink soliton solutions explicit expressions one- and two-soliton solutions are derived for particular column solutions. Different profiles of kink-kink and, kink and anti-kink interactions are illustrated for a different parameters and arbitrary functions. First-order bound state solution is also displayed in our work.
Cite
@article{arxiv.2102.05835,
title = {Dynamics of kink-soliton solutions for $2+1$-dimensional sine-Gordon equation},
author = {U. Saleem and H. Sarfraz and Y. Hanif},
journal= {arXiv preprint arXiv:2102.05835},
year = {2022}
}