Solitary waves with Galilean invariance in dispersive shallow-water flows

The present work deals with a recently derived nonlinear dispersive system for shallow-water flows. Unlike the classical Boussinesq models, the new one possesses Galilean invariance. It is investigated numerically by means of a conservative difference scheme. In order to understand the intrinsic physical mechanisms behind the balance between nonlinearity and dispersion larger phase speeds of the solitary waves are considered which are formally beyond the applicability of the weakly nonlinear approximation. The pseudo-particle behavior of the solitary waves is interrogated. It is shown that the system with Galilean invariance is, in a sense, more "elastic" than the classical Boussinesq model. Snap-shots of the interactions of the localized waves are presented graphically. The phase shifts experienced by the pseudo-particles are shown to be of the opposite sign to these for systems without Galilean invariance.