TY - JOUR
T1 - KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation
JF - Mathematische Annalen
Y1 - 2014
A1 - P Baldi
A1 - Massimiliano Berti
A1 - Riccardo Montalto
AB - We prove the existence of small amplitude quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of the linear Airy equation. For Hamiltonian or reversible nonlinearities we also prove their linear stability. The key analysis concerns the reducibility of the linearized operator at an approximate solution, which provides a sharp asymptotic expansion of its eigenvalues. For quasi-linear perturbations this cannot be directly obtained by a KAM iteration. Hence we first perform a regularization procedure, which conjugates the linearized operator to an operator with constant coefficients plus a bounded remainder. These transformations are obtained by changes of variables induced by diffeomorphisms of the torus and pseudo-differential operators. At this point we implement a Nash-Moser iteration (with second order Melnikov non-resonance conditions) which completes the reduction to constant coefficients. © 2014 Springer-Verlag Berlin Heidelberg.
N1 - cited By (since 1996)0; Article in Press
ER -