Multi-solitonic solutions for the variable-coefficient variant Boussinesq model of the nonlinear water waves |
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Authors: | Lei Wang Yi-Tian Gao Feng-Hua Qi |
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Institution: | a State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China b Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China c School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China |
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Abstract: | For the nonlinear and dispersive long gravity waves traveling in two horizontal directions with varying depth of the water, we consider a variable-coefficient variant Boussinesq (vcvB) model with symbolic computation. We construct the connection between the vcvB model and a variable-coefficient Ablowitz-Kaup-Newell-Segur (vcAKNS) system under certain constraints. Using the N-fold Darboux transformation of the vcAKNS system, we present two sets of multi-solitonic solutions for the vcvB model, which are expressed in terms of the Vandermonde-like and double Wronskian determinants, respectively. Dynamics of those solutions are analyzed and graphically discussed, such as the parallel solitonic waves, shape-changing collision, head-on collision, fusion-fission behavior and elastic-fusion coupled interaction. |
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Keywords: | Variable-coefficient variant Boussinesq model Multi-solitonic solutions N-fold Darboux transformation Vandermonde-like determinant Double Wronskian determinant Symbolic computation |
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