Speaker: Robert Jenkins (UCF, Mathematics Dept)
Title: Talanov self-focusing in the focusing nonlinear Schrödinger hierarchy.
Abstract: I’ll describe some recent work in which we investigate the small dispersion limit behavior of parabolic pulse initial data for the focusing NLS equation. Talanov showed in the 1960s that such initial data exhibit singular self-focusing with finite-time blow up of their amplitude. Suleimanov recently proposed a mechanism for the dispersive regularization of this blow up. I’ll discuss our proof of Suleimanov’s regularization for NLS. We’ll also discuss how this phenomena extends to the higher order flows on the integrable hierarchy.
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