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- Title
Dynamics of kink-soliton solutions of the -dimensional sine-Gordon equation.
- Authors
Saleem, U.; Sarfraz, H.; Hanif, Y.
- Abstract
We study the dynamics of explicit solutions of the -dimensional (2D) sine-Gordon equation. The Darboux transformation is applied to the associated linear eigenvalue problem to construct nontrivial solutions of the D sine-Gordon equation in terms of a ratio of determinants. We obtain a generalized expression for an -fold transformed dynamical variable, which enables us to calculate explicit expressions of nontrivial solutions. To explore the dynamics of kink soliton solutions, explicit expressions for one- and two-soliton solutions are derived for particular column solutions. Different profiles of kink–kink and kink–anti-kink interactions are illustrated for different parameters and arbitrary functions. We also present a first-order bound state solution.
- Subjects
SINE-Gordon equation; DARBOUX transformations; ARBITRARY constants; BOUND states; EIGENVALUES
- Publication
Theoretical & Mathematical Physics, 2022, Vol 210, Issue 1, p68
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1134/S0040577922010056