Inelastic interactions and double Wronskian solutions for the Whitham–Broer–Kaup model in shallow water

Abstract

Under investigation in this paper is the Whitham–Broer–Kaup (WBK) model for the dispersive long wave in shallow water. Connection between the WBK model and a second-order Ablowitz–Kaup–Newell–Segur (AKNS) system is revealed. By means of the Darboux transformation for the second-order AKNS system, the multisoliton solutions in terms of the double Wronskian determinant for the WBK model are derived. Inelastic interactions are graphically discussed. Our results could be helpful for interpreting certain nonlinear wave phenomena in shallow water.