Speaker: Catherine Sulem, University of Toronto
Date: December 3, 2015
Title: Normal forms transformations for water waves
Abstract: We consider the equations of water waves in a two-dimensional channel of finite or infinite depth, in the setting of spatially periodic solutions. These equations are seen in the framework of Hamiltonian systems, for which the Hamiltonian energy has a convergent Taylor expansion in canonical variables near the equilibrium solution. We give an analysis of the Birkhoff normal form transformation that eliminates third-order non-resonant terms of the Hamiltonian. We also provide an analysis of the dynamics of remaining resonant triads in certain cases. This is joint work with Walter Craig (McMaster University).