**Title:** Quasi periodic solutions of quasi linear and fully nonlinear forced perturbations of Airy-KdV equation

**Abstract:** I will present a recent result concerning existence and stability of quasi periodic small amplitude solutions of quasi linear and fully nonlinear forced perturbations of the Airy KdV equation, for a Cantor-like set of frequencies of asymptotically full Lebesgue measure. The proof is based on a Nash-Moser implicit function Theorem in Sobolev class, whose main difficulty is to solve the linearized equation at any approximate solutions. The key idea is a reduction procedure which conjugates the linearized operator (at any approximate solution) to a constant coefficients diagonal operator.

This seminar is part of the AJS series of seminars.