Formula omitted]-soliton solutions and localized structures for the [formula omitted]-dimensional Broer–Kaup–Kupershmidt system

Abstract

In this paper, the ( 2 + 1 ) -dimensional Broer–Kaup–Kupershmidt system is investigated by means of Bäcklund transformation and the Hirota bilinear method. With symbolic computation, the N -soliton solutions with N + 1 arbitrary functions for that system are derived. Based on the derived solutions, some soliton structures, localized structures and special fission interaction behaviour are graphically studied, which might be helpful to understand the propagation processes for nonlinear and dispersive long waves in shallow water.