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A variational approach to surface solitary waves. (English) Zbl 0574.76015
This paper makes rigorous use of a variational procedure to obtain periodic and solitary surface waves in a fluid with a non-diffusive variable density which may be discontinuous. The principle used is Lagrangian in character and reduces to a constrained variational problem. In addition to obtaining a single crested wave moving in a fluid which is at rest far from the crest, periodic solutions are also found in the horizontal direction which decay exponentially from crest to trough.
Reviewer: A.Jeffrey

MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25 Solitary waves for incompressible inviscid fluids
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