Analysis Seminar

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Hamiltonians and Normal Forms for Water Waves

Speaker: Walter Craig, McMaster University

Location: Warren Weaver Hall 1302

Date: Thursday, December 8, 2016, 11 a.m.

Synopsis:

It was shown by VE Zakharov that the equations for water waves can be posed as a Hamiltonian dynamical system, and that the equilibrium solution is an elliptic stationary point. This talk will discuss two aspects of the water wave equations in this context. Firstly, we generalize the formulation of Zakharov to include overturning wave profiles, answering a question posed by T. Nishida. Secondly, we will discuss the question of Birkhoff normal forms for the water waves equations in the setting of spatially periodic solutions, including the function space mapping properties of these transformations.