Various aspects of the dynamics of the cubic Szegö solutions
Apparaît également dans la collection : Asymptotic analysis of evolution equations / Analyse asymptotique des équations d'évolution
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. 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.
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