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Existence by minimisation of solitary water waves on an ocean of infinite depth. (English) Zbl 1109.76013
Summary: 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
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References:
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