JournalsemssVol. 12, No. 1pp. 215–242

On the Kaup–Broer–Kupershmidt systems

  • Christian Klein

    Université de Bourgogne, Dijon, France; Institut Universitaire de France, Paris, France
    ORCID

  • Jean-Claude Saut

    Université Paris-Saclay et CNRS, Orsay, France
    ORCID
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Abstract

The aim of this paper is to survey and complete, mostly by numerical simulations, results on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. It is the only member of the so-called () family of Boussinesq systems known to be completely integrable.

Cite this article

Christian Klein, Jean-Claude Saut, On the Kaup–Broer–Kupershmidt systems. EMS Surv. Math. Sci. 12 (2025), no. 1, pp. 215–242

DOI 10.4171/EMSS/98