| Abstract: |
| In this talk, we present the derivation of a Hamiltonian Dysthe equation for the slowly varying envelope of modulated wavetrains based on a Hamiltonian formulation of the water wave problem and by applying techniques from Hamiltonian theory. The models we consider include 2d and 3d surface gravity waves and 2d water waves with constant vorticity. Our method provides a procedure to reconstruct the surface elevation from the wave envelope, based on the Birkhoff normal form transformation to eliminate all non-resonant triads.
The talk is based on a series of works with Catherine Sulem (University of Toronto) and Philippe Guyenne (University of Delaware). |
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