Solitary waves with Galilean invariance in dispersive shallow-water flows. (Q2754431)

In the last about ten years, the author established and used a new model for the dispersive shallow-water system appearing in long-wave models of inviscid fluid with free surface. The novelty of this model is that it preserves the Galilean invariance of the motion. This is the main advantage over the Boussinesq system of equations describing such motions. The derived system with Galilean conservation laws is compared with the Boussinesq system, and a conservative difference scheme is constructed for the approximate solution in the Galilean invariant case; its efficiency is proved. The study gives numerical solutions in four different cases, ordered after the nonlinearity of the motions represented by some parameters. The results are presented in four double plots, Galilean and Boussinesq, depicting the snapshots of the wave system and the trajectories of the centers of solitary waves for different values of parameters.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00018].