Abstract
In this paper, we derive the Lax pair associated with the Whitham–Broer–Kaup equations. Based on the Lax pair obtained, we construct the Darboux transformation with multi-parameters and obtain the one- and multi-soliton solutions. In addition, we qualitatively analyze various types of interaction behavior between two solitary waves along with graphical demonstration, in order to provide valuable information on the shallow water motion.
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