# Analysis and PDE seminar: Babenko's equation for periodic gravity waves on water of finite

Guest lecture

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

depth

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.