Speaker: Vera Hur, UIUC
Date: October 22, 2020
Title: Unstable Stokes waves: a periodic Evans function approach
Abstract: I will discuss spectral instability of a Stokes wave of small amplitude in the finite depth. Analysis of a periodic Evans function near the origin of the spectral plane offers an alternative proof of the Benjamin-Feir instability. Analysis near the resonance of order 2 reveals spectral instability when 0.8644...<(wave number)x(depth)<1.0079.... The Benjamin-Feir instability occurs when (wave number)x(depth)>1.3627..., so new unstable waves are found. This seems the first rigorous proof of such high-frequency instability. Joint work with Z. Yang.