A completely integrable toy model of nonlinear Schrodinger equations without dispersion
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| Description: |
Gerard, P (Universite Paris-Sud)
Tuesday 26 October 2010, 14:00-14:45 |
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| Created: | 2010-10-27 12:41 | ||||
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| Collection: | Partial Differential Equations in Kinetic Theories | ||||
| Publisher: | Isaac Newton Institute | ||||
| Copyright: | Gerard, P | ||||
| Language: | eng (English) | ||||
| Credits: |
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| Abstract: | 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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