@article {Baldi20141,
title = {KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation},
journal = {Mathematische Annalen},
year = {2014},
note = {cited By (since 1996)0; Article in Press},
pages = {1-66},
abstract = {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. {\textcopyright} 2014 Springer-Verlag Berlin Heidelberg.},
issn = {00255831},
doi = {10.1007/s00208-013-1001-7},
author = {P Baldi and Massimiliano Berti and Riccardo Montalto}
}
@article {2014,
title = {KAM for quasi-linear KdV},
journal = {C. R. Math. Acad. Sci. Paris},
volume = {352},
number = {Comptes Rendus Mathematique;volume 352; issue 7-8; pages 603-607;},
year = {2014},
pages = {603-607},
publisher = {Elsevier},
abstract = {We prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

},
doi = {10.1016/j.crma.2014.04.012},
url = {http://urania.sissa.it/xmlui/handle/1963/35067},
author = {P Baldi and Massimiliano Berti and Riccardo Montalto}
}
@article {2014,
title = {KAM for Reversible Derivative Wave Equations},
journal = {Arch. Ration. Mech. Anal.},
volume = {212},
number = {Archive for rational mechanics and analysis;volume 212; issue 3; pages 905-955;},
year = {2014},
pages = {905-955},
publisher = {Springer},
abstract = {We prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

},
doi = {10.1007/s00205-014-0726-0},
url = {http://urania.sissa.it/xmlui/handle/1963/34646},
author = {Massimiliano Berti and Luca Biasco and Michela Procesi}
}
@article {Berti2013301,
title = {KAM theory for the Hamiltonian derivative wave equation},
journal = {Annales Scientifiques de l{\textquoteright}Ecole Normale Superieure},
volume = {46},
number = {2},
year = {2013},
note = {cited By (since 1996)4},
pages = {301-373},
abstract = {We prove an infinite dimensional KAM theorem which implies the existence of Can- tor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. {\textcopyright} 2013 Soci{\'e}t{\'e} Math{\'e}matique de France.

},
issn = {00129593},
author = {Massimiliano Berti and Luca Biasco and Michela Procesi}
}