Post-edited Various aspects of the dynamics of the cubic Szegö solutions
Auteurs : Grellier, Sandrine (Auteur de la Conférence)
CIRM (Editeur )
Résumé : The cubic Szegö equation has been introduced as a toy model for totally non dispersive evolution equations. It turned out that it is a complete integrable Hamiltonian system for which we built a non linear Fourier transform giving an explicit expression of the solutions.Codes MSC :
This explicit formula allows to study the dynamics of the solutions. We will explain different aspects of it: almost-periodicity of the solutions in the energy space, uniform analyticity for a large set of initial data, turbulence phenomenon for a dense set of smooth initial data in large Sobolev spaces.
From joint works with Patrick Gérard.
35B15 - Almost and pseudo-almost periodic solutions of PDE
35B40 - Asymptotic behavior of solutions of PDE
35Q55 - NLS-like equations (nonlinear Schrödinger)
37K15 - Integration of completely integrable systems by inverse spectral and scattering methods
47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators