Analysis and PDE seminar: Babenko's equation for periodic gravity waves on water of finite
Speaker: Nikolay Kuznetsov, Researcher, Laboratory for Mathematical
Modelling of Wave Phenomena,
Institute for Problems in Mechanical Engineering, Russian Academy of
Sciences, St. Petersburg
Title: Babenko's equation for periodic gravity waves on water of finite
Abstract: For the nonlinear two-dimensional problem, describing periodic
steady waves on water of finite depth in the absence of surface tension,
a single pseudo-differential operator equation (Babenko's equation) is
considered. This equation has the same form as the equation for waves
on infinitely deep water; the latter had been proposed by Babenko in
1987 and studied in detail by Buffoni, Dancer and Toland in 2000.
Unlike the equation for deep water involving just the $2 \pi$-periodic
Hilbert transform C, the equation to be presented in the talk contains
an operator which is the sum of C and a compact operator depending on
the depth of water.