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arXiv · 2102.05835

Dynamics of kink-soliton solutions for $2+1$-dimensional sine-Gordon equation

U. Saleem·H. Sarfraz·Y. Hanif
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Abstract

In this paper we study the dynamics of explicit solutions of $2+1$-dimensional ($2$D) sine-Gordon equation. The Darboux transformation is applied to the associated linear eigenvalue problem to construct nontrivial solutions of $2$D sine-Gordon equation in terms of ratios of determinants. We obtained a generalized expression for $N$-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.

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U. Saleem, H. Sarfraz, Y. Hanif. 2021-02-11. Dynamics of kink-soliton solutions for $2+1$-dimensional sine-Gordon equation. https://doi.org/10.1134/s0040577922010056

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