Multi-solitonic solutions for the variable-coefficient variant Boussinesq model of the nonlinear water waves

作者：Wang Lei; Gao Yi Tian^*; Qi Feng Hua

来源：Journal of Mathematical Analysis and Applications, 2010, 372(1): 110-119.

DOI：10.1016/j.jmaa.2010.06.016

• Variable-coefficient variant Boussinesq model
• Multi-solitonic solutions
• N-fold Darboux transformation
• Vandermonde-like determinant
• Double Wronskian determinant
• Symbolic computation

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.

• 单位
  北京大学