Existence by minimisation of solitary water waves on an ocean of infinite depth.

*(English)*Zbl 1109.76013Summary: The abstract minimisation method introduced in a recent work by E. Séré, J.F. Toland and the author [Minimisation methods for quasi-linear problems, with an application to periodic water waves, preprint] gives a new proof of the existence of capillary-gravity solitary water waves on the surface of a two-dimensional ocean of infinite depth. This problem was first studied by G. Iooss and P. Kirrmann [Arch. Ration. Mech. Anal. 136, 1–19 (1998; Zbl 0879.76011)] in the setting of normal form theory for reversible infinite-dimensional “spatial” dynamical systems.

##### MSC:

76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |

35B38 | Critical points of functionals in context of PDEs (e.g., energy functionals) |

35A15 | Variational methods applied to PDEs |

35Q35 | PDEs in connection with fluid mechanics |

35S10 | Initial value problems for PDEs with pseudodifferential operators |

47J30 | Variational methods involving nonlinear operators |

##### References:

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