The Darboux transformation and soliton solutions for a new (2+1)-dimensional variant Boussinesq system in shallow water with symbolic computation

Abstract

A new (2+1)-dimensional variant Boussinesq system with its spectral problems is presented in this paper, which has a close connection with the Whitham–Broer–Kaup soliton hierarchy describing long waves in shallow water. Based on the associated spectral problems, the Darboux transformation (DT) with multi-parameters was firstly constructed with the help of symbolic computation. Then, by using the DT, some new one- and two-soliton solutions of the (2+1)-dimensional variant Boussinesq system were obtained and graphically represented. These solutions might be of some value in fluid dynamics.