N-soliton Solutions and Nonlinear Dynamics for a Generalized Broer–Kaup System

Water waves are observed in many situations, as well as on rivers, lakes or oceans. Under consideration in this paper is a famous dispersion water wave model: the (1 + 1)-dimensional generalized Broer–Kaup (gBK) system. This system is used to simulate the bi-directional propagation of long waves in shallow water. Based on the bilinear forms given in this paper, novel N-soliton solutions of this gBK system is obtained by using Hirota's bilinear method. In order to understand the nonlinear dynamics localized in the gBK systems, local structures of the obtained one-, two-, three- and four-soliton solutions are shown. This paper reveals the local structures of the one-soliton solutions and interactions between multi-soliton solutions and preliminarily explains the nonlinear dynamical characteristics of bell soliton and kink soliton in this gBK system.