Geodesic
Dynamics of kink-soliton solutions of the~$(2+1)$-dimensional
Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 1, pp. 80-98

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We study the dynamics of explicit solutions of the $(2+1)$-dimensional (2D) sine-Gordon equation. The Darboux transformation is applied to the associated linear eigenvalue problem to construct nontrivial solutions of the $2$D sine-Gordon equation in terms of a ratio of determinants. We obtain a generalized expression for an $N$-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.
Keywords: integrable systems
Mots-clés : sine-Gordon equation, solitons, Darboux transformation. 
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     author = {U. Saleem and H. Sarfraz and Ya. Hanif},
     title = {Dynamics of kink-soliton solutions of the~$(2+1)$-dimensional},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {210},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_210_1_a4/}
}
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U. Saleem; H. Sarfraz; Ya. Hanif. Dynamics of kink-soliton solutions of the~$(2+1)$-dimensional. Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 1, pp. 80-98. http://geodesic.mathdoc.fr/item/TMF_2022_210_1_a4/