Abstract
Recent studies on the water waves have been impressive. Of current interest in fluid physics, Jiang et al. [J. Math. Phys. 51, 093519 (2010)] have reported certain soliton interactions along with binary-Bell-polynomial-type Bäcklund transformation and Lax pair for the (2 + 1)-dimensional Boiti-Leon-Pempinelli system for water waves. However, the story introduced by that paper can be made more complete, since in fluid physics and other fields, the variable-coefficient models can describe many physical processes more realistically than their constant-coefficient counterparts. Hereby, on a (2 + 1)-dimensional variable-coefficient Boiti-Leon-Pempinelli generalization, water-wave symbolic computation is performed. For the horizontal velocity of the water wave as well as the wave elevation, variable-coefficient-dependent auto-Bäcklund transformation is constructed out, along with some variable-coefficient-dependent shock-wave-type solutions. Relevant variable-coefficient constraints are also given, with respect to water waves.
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