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A completely integrable toy model of nonlinear Schrodinger equations without dispersion

Gerard, P (Universite Paris-Sud)
Tuesday 26 October 2010, 14:00-14:45

Seminar Room 1, Newton Institute


I shall discuss the cubic Szego equation which is the Hamiltonian evolution associated to the L^4 norm on the Hardy space of the circle, and explain why it is a toy model for NLS without dispersion. I shall prove that this evolution admits a Lax pair, and use this structure to solve explicitely the Cauchy problem through some inverse spectral problem, and discuss various stability questions.

This is a joint work with Sandrine Grellier (Orleans)


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