Session S22 - Deterministic and probabilistic aspects of nonlinear evolution equations

Thursday, July 22, 16:00 ~ 16:30 UTC-3

Normal form transformations and Dysthe's equation for the nonlinear modulation of deep-water gravity waves

Catherine Sulem

University of Toronto, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

I will present a new Hamiltonian version of Dysthe's equation for weakly modulated gravity waves on deep water. A key ingredient in this derivation is a Birkhoff normal form transformation that eliminates all non-resonant cubic terms and allows for a non-perturbative reconstruction of the free surface. This modulational approximation is tested against numerical solutions of the classical Dysthe's equation and against direct numerical simulations of Euler's equations for nonlinear water waves. An alternate spatial form is proposed and tested against laboratory experiments on short-wave packets. (joint work with W. Craig, P. Guyenne, A. Kairzhan, B. Xu)

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