This article is cited in 2 papers

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

Hui Mao

School of Mathematics and Statistics, Nanning Normal University, Nanning, China

Abstract: 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.

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

MSC: 35C08

Received: 01.07.2020
Revised: 04.08.2020

DOI: 10.4213/tmf9949

 English version: Theoretical and Mathematical Physics, 2020, 205:3, 1638–1651

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