Integrability and wave turbulence for Hamiltonian partial differential equations

School of Mathematics Colloquium
Tuesday, February 9, 2016 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 005
Patrick Gerard – UniversitĂ© Paris-Sud – patrick.gerard@math.u-psud.fr
Michael Damron
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. .