Abstract
Under investigation in this paper, with symbolic computation, is the Whitham–Broer–Kaup (WBK) system for the dispersive long waves in the shallow water small-amplitude regime. N-fold Darboux transformation (DT) for a spectral problem associated with the WBK system is constructed. Odd-soliton solutions in terms of the Vandermonde-like determinant for the WBK system are presented via the N-fold DT and evolution of the three-soliton solutions is graphically studied. Our results could be used to illustrate the bidirectional propagation of the waves in the shallow water small-amplitude regime.
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