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.

Keywords

Bibliographic record

BibTeX Citation

@article{Durn2013galileaninvariance,
  author = {Durán, A. and Dutykh, D. and Mitsotakis, D.},
  title = {On the Galilean invariance of some dispersive wave equations},
  journal = {Stud. Appl. Math.},
  year = {2013},
  volume = {131},
  number = {4},
  pages = {359--388},
  doi = {10.1111/sapm.12015},
  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.},
  keywords = {Boussinesq equations, BBM equation, surface water waves, water waves, solitary waves, dispersive wave equations, fluid dynamics, wave propagation, Boussinesq system, Euler equations, Galilean invariance, dispersive waves, Peregrine system}
}