3pm - 4pm
Tuesday 1 May 2018
An estimate for the Morse index of a Stokes wave and the Khuri-Martin-Wu conjecture
Professor Eugene Shargorodsky (Kings College London) will be speaking.
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- Professor Eugene Shargorodsky (Kings College London)
Stokes waves are steady periodic water waves on the free surface of an infinitely deep irrotational two-dimensional flow under gravity without surface tension. They can be described in terms of solutions of the Euler-Lagrange equation of a certain functional.
This allows one to define the Morse index of a Stokes wave. B. Buffoni, E.N. Dancer, and J.F. Toland (2000) proved, using earlier results by P.I. Plotnikov (1991), that if the Morse indices of the elements of a set of non-singular Stokes waves are bounded, then none of them is close to a singular one.
I will present a quantitative version of this result and explain its connection to the proof of a conjecture by N.N. Khuri, A. Martin and T.T. Wu (2001) on the number of bound states in two dimensions.