Integrability and wave turbulence for Hamiltonian partial differential equations

Series: 
School of Mathematics Colloquium
Tuesday, February 9, 2016 - 15:30
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Université Paris-Sud
,  
Organizer: 
In the world of Hamiltonian partial differential equations, complete integrability is often associated to rare and peaceful dynamics, while wave turbulence rather refers to more chaotic dynamics. In this talk I will first try to give an idea of these different notions. Then I will  discuss the example of the cubic Szegö equation, a nonlinear wave toy model which surprisingly displays both properties. The key is a Lax pair structure involving Hankel operators from classical analysis, leading to the inversion of large ill-conditioned matrices. .