Obtaining multisoliton solutions of the $(2+1)$-dimensional Camassa–Holm system using Darboux transformations

Hui Mao

Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 3, pp. 451-466

Résumé

We construct and study Darboux transformations for the $(2+1)$-dimensional Camassa–Holm system. We apply a reciprocal transformation that relates the $(2+1)$-dimensional Camassa–Holm system and the linear system associated with the modified Kadomtsev–Petviashvili hierarchy. Using three Darboux transformation operators, we obtain three types of solutions for the $(2+1)$-dimensional Camassa–Holm system, of which one is a multisoliton solution. In addition, we briefly discuss rational solutions.

Détail

Keywords: $(2+1)$-dimensional Camassa–Holm system, reciprocal transformation
Mots-clés : Darboux transformation, soliton solution.

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