Differential Equations Seminar

I will discuss a new periodic Evans function approach for cylindrical domains, and its application to the spectral instability of Stokes waves in the finite depth. Numerical evidence suggests instability whenever the unperturbed wave is 'resonant' with its infinitesimal perturbation waves. This has not been studied analytically except the Benjamin-Feir instability, near the origin of the spectral plane, when (wave number)x(depth)>1.3627... for small amplitude. I will discuss an alternative proof of the Benjamin-Feir instability and, also, the first proof of spectral instability away from the origin, when 0.86430... Speaker(s): Vera Hur (UIUC)