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Asymptotic integrability of water waves. (English) Zbl 0982.76511
Summary: The asymptotic integrability of the idealized water waves is formally established. Namely, it is shown that in the small amplitude, long wave limit there exists an explicit transformation which maps these equations to a system of two integrable equations. It is also shown that the concepts of master symmetries and of bi-Hamiltonian structures can be used to obtain similar results for other physical systems.

MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
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