Cauchy problem for dispersive equations

I have been interested in the local or global in time Cauchy problem in some Sobolev spaces for various dispersive equations in the class of non-linear Schrödinger equations coupled to matter equations. Some asymptotic limit equations have been investigated.

I also studied a general framework for the Poisson’s recurrence for Hamiltonian equations and their numerical time discretizations.

More recently I addressed the $p$-Schrödinger equation for the modelling of Newton’s cradle.

My PhD thesis deals with the theme, as well as part of my Habilitation thesis.