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Vera Hur: Unstable Stokes waves: a periodic Evans function approach

Submitted by Jorge Cisneros on October 22, 2020 - 11:00am
Vera Hur

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.

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