01372nas a2200145   4500008004100000245007300041210006900114260003400183520083400217653001701051100001301068700002401081700002301105856009801128       2013                        en  d00aA note on KAM theory for quasi-linear and fully nonlinear forced KdV0 anote on KAM theory for quasilinear and fully nonlinear forced Kd  bEuropean Mathematical Society3 aWe 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.10aKAM for PDEs1 aBaldi, P1 aBerti, Massimiliano1 aMontalto, Riccardo  uhttps://math.sissa.it/publication/note-kam-theory-quasi-linear-and-fully-nonlinear-forced-kdv