%0 Journal Article
%J Mathematische Annalen
%D 2014
%T KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation
%A P Baldi
%A Massimiliano Berti
%A Riccardo Montalto
%X 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.
%B Mathematische Annalen
%P 1-66
%G eng
%R 10.1007/s00208-013-1001-7
%0 Journal Article
%J C. R. Math. Acad. Sci. Paris
%D 2014
%T KAM for quasi-linear KdV
%A P Baldi
%A Massimiliano Berti
%A Riccardo Montalto
%X We prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

%B C. R. Math. Acad. Sci. Paris
%I Elsevier
%V 352
%P 603-607
%G en
%U http://urania.sissa.it/xmlui/handle/1963/35067
%N 7-8
%1 35302
%2 Mathematics
%4 1
%$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-11-30T15:30:40Z (GMT) No. of bitstreams: 0
%R 10.1016/j.crma.2014.04.012