Abstract
It is established that the Whitham–Broer–Kaup shallow water system and the “resonant” nonlinear Schrodinger equation are equivalent. A symmetric integrable 2+1-dimensional version of the Whitham–Broer–Kaup system is constructed which, in turn, is equivalent to a recently introduced resonant Davey–Stewartson I system incorporating a Madelung–Bohm type quantum potential. A bilinear representation is adopted and resonant solitonic interaction in this new 2+1-dimensional Kaup–Broer system is exhibited.
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