Integrability versus Wave Turbulence in Hamiltonian partial differential equations

Integrability versus Wave Turbulence in Hamiltonian partial differential equations

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Patrick Gerard , University of Paris-Sud
Fine Hall 314

In the world of Hamiltonian partial differential equations, complete integrability and wave turbulence are often considered as opposite paradigms. The purpose of this talk is to give a rough idea of these different notions, and to discuss the example of a nonlinear wave toy model which surprisingly displays both properties. The key is a Lax pair structure involving Hankel operators from classical analysis, and is connected to a surprisingly explicit inverse spectral method.