A completely integrable toy model of nonlinear Schrodinger equations without dispersion
Seminar Room 1, Newton Institute
AbstractI 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)