Seminari del Dipartimento

Analisi

I present a new result on the existence and the stability of small amplitude quasi-periodic solutions for Hamiltonian perturbations of the Degasperis-Procesi equation under periodic boundary conditions.
These solutions are constructed by a hard Implicit Function Nash-Moser Theorem, based on a Newton-type algorithm. The main issue in implementing this iterative scheme  is the inversion of the linearized operator in a neighborhood of the origin. The analysis of the linearized operator requires to solve quasi-periodic transport equations and to exploit some pseudo differential calculus techniques.
To initialize the Nash-Moser scheme we need to perform a bifurcation analysis by means of a Birkhoff normal form procedure.
The Degasperis-Procesi equation presents some non trivial Birkhoff resonances and we show how to overcome this problem by exploiting the integrability of the unperturbed system.
This is a joint work with Roberto Feola and Michela Procesi.
 
org: PROCESI Michela