GAUGE TRANSFORMATION AND SOLITON SOLUTIONS FOR THE WHITHAM–BROER–KAUP SYSTEM IN THE SHALLOW WATER

Abstract

In the shallow-water studies, the Whitham–Broer–Kaup (WBK) system can be used to describe the propagation of the long waves. In this paper, based on the Lax pair of the WBK system, we derive the gauge transformation from the WBK system to the Ablowitz–Kaup–Newell–Segur (AKNS) system with the help of symbolic computation. Applying the Darboux transformation of the AKNS system, we obtain some soliton solutions of the WBK system. Those results might be useful in the investigations on the propagation of solitons in such situation as shallow water.