@article {Berti2013199,
	title = {Existence and stability of quasi-periodic solutions for derivative wave equations},
	journal = {Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni},
	volume = {24},
	number = {2},
	year = {2013},
	note = {cited By (since 1996)0},
	pages = {199-214},
	abstract = {In this note we present the new KAM result in [3] which proves the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. In turn, this result is derived by an abstract KAM theorem for infinite dimensional reversible dynamical systems*.},
	keywords = {Constant coefficients, Dynamical systems, Existence and stability, Infinite dimensional, KAM for PDEs, Linearized equations, Lyapunov exponent, Lyapunov methods, Quasi-periodic solution, Small divisors, Wave equations},
	issn = {11206330},
	doi = {10.4171/RLM/652},
	author = {Massimiliano Berti and Luca Biasco and Michela Procesi}
}
@article {2013,
	title = {A note on KAM theory for quasi-linear and fully nonlinear forced KdV},
	journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 3: 437{\textendash}450},
	year = {2013},
	publisher = {European Mathematical Society},
	abstract = {We present the recent results in [3] concerning quasi-periodic solutions
for quasi-linear and fully nonlinear forced perturbations of KdV equations.
For Hamiltonian or reversible nonlinearities the solutions are linearly stable.
The proofs are based on a combination of di erent ideas and techniques:
(i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization
procedure, which conjugates the linearized operator to a di erential operator
with constant coe cients plus a bounded remainder. These transformations
are obtained by changes of variables induced by di eomorphisms of the torus
and pseudo-di erential operators. (iii) A reducibility KAM scheme, which
completes the reduction to constant coe cients of the linearized operator,
providing a sharp asymptotic expansion of the perturbed eigenvalues.},
	keywords = {KAM for PDEs},
	doi = {10.4171/RLM/660},
	author = {P Baldi and Massimiliano Berti and Riccardo Montalto}
}
