XXIX Workshop on Geometric Methods in Physics 27.06-03.07.2010

Marco Marco Bertola

Universality in the profile of small-dispersion integrable waves: the focusing Nonlinear Schroedinger equation.

The goal of the talk is to explain recent results on the small dispersion limit of the focusing nonlinear Schroedinger equation. This includes a (partial) proof of Dubrovin's conjecture regarding the role of a special solution of the Painleve' 1 equation near the point of gradient catastrophe. Oddly, similar universality results occur in the seemingly unrelated area of random matrices.

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