@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}
}
