On the Galilean invariance of some dispersive wave equations

Abstract

Surface water waves in ideal fluids have been typically modeled by asymptotic approximations of the full Euler equations. Some of these simplified models lose relevant properties of the full water wave problem. One of them is the Galilean symmetry, which is not present in important models such as the BBM equation and the Peregrine (Classical Boussinesq) system. In this paper we propose a mechanism to modify the above mentioned classical models and derive new, Galilean invariant models. We present some properties of the new equations, with special emphasis on the computation and interaction of their solitary-wave solutions. The comparison with full Euler solutions shows the relevance of the preservation of Galilean invariance for the description of water waves.

29 pages, 13 figures, 2 tables, 71 references. Other author papers can be downloaded at http://www.denys-dutykh.com/

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• Peregrine's system revisited
• Global weak solutions of a Hamiltonian regularised Burgers equation
• Asymptotic nonlinear and dispersive pulsatile flow in elastic vessels with cylindrical symmetry
• Galilean-transformed solitons and supercontinuum generation in dispersive media
• On time relaxed schemes and formulations for dispersive wave equations