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Multi-solitonic solutions for the variable-coefficient variant Boussinesq model of the nonlinear water waves. (English) Zbl 1425.76044

Summary: 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.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35C08 Soliton solutions
35A25 Other special methods applied to PDEs
35A22 Transform methods (e.g., integral transforms) applied to PDEs
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