Symbolic computation on the long gravity water waves: scaling transformations, bilinear forms, N-soliton solutions and auto-Bäcklund transformation for a variable-coefficient variant Boussinesq system

Xin-Yi Gao, Yong-Jiang Guo and Wen-Rui Shan

Chaos, Solitons & Fractals, 2021, vol. 152, issue C

Abstract: Water waves are one of the most common phenomena in nature. Hereby, on a variable-coefficient variant Boussinesq system for the nonlinear and dispersive long gravity waves travelling in two horizontal directions in the shallow water with varying depth, with respect to the horizontal velocity of the water and height deviating from the equilibrium position of the water, our symbolic computation leads to the scaling transformations, bilinear forms, N-soliton solutions and auto-Bäcklund transformation with the sample solitons, where N is a positive integer. Our results are dependent on the water-wave variable coefficients and under the relevant variable-coefficient constraints.

Keywords: Long gravity water waves; Symbolic computation; Variable-coefficient variant Boussinesq system; Scaling transformations and bilinear forms via the binary Bell polynomials; Bäcklund transformation; Solitonic solutions (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007463

DOI: 10.1016/j.chaos.2021.111392

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