An integrable evolution equation for surface waves in deep water
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Data
2014-01-17
Autores
Kraenkel, R. A. [UNESP]
Leblond, H.
Manna, M. A.
Título da Revista
ISSN da Revista
Título de Volume
Editor
Iop Publishing Ltd
Resumo
In order to describe the dynamics of monochromatic surface waves in deep water, we derive a nonlinear and dispersive system of equations for the free surface elevation and the free surface velocity from the Euler equations in infinite depth. From it, and using a multiscale perturbative method, an asymptotic model for small wave steepness ratio is derived. The model is shown to be completely integrable. The Lax pair, the first conserved quantities as well as the symmetries are exhibited. Theoretical and numerical studies reveal that it supports periodic progressive Stokes waves which peak and break in finite time. Comparison between the limiting wave solution of the asymptotic model and classical results is performed.
Descrição
Palavras-chave
integrable systems, multi-scale methods, deep water, gravity waves
Como citar
Journal Of Physics A-mathematical And Theoretical. Bristol: Iop Publishing Ltd, v. 47, n. 2, 17 p., 2014.