We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear (also called strongly nonlinear) autonomous Hamiltonian differentiable perturbations of the mKdV equation. The proof is based on a weak version of the Birkhoff normal form algorithm and a nonlinear Nash–Moser iteration. The analysis of the linearized operators at each step of the iteration is achieved by pseudo-differential operator techniques and a linear KAM reducibility scheme.
KAM for autonomous quasi-linear perturbations of mKdV / Baldi, Pietro; Berti, Massimiliano; Montalto, Riccardo. - In: BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA. - ISSN 1972-6724. - 9:2(2016), pp. 143-188. [10.1007/s40574-016-0065-1]
KAM for autonomous quasi-linear perturbations of mKdV
BALDI, PIETRO;
2016
Abstract
We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear (also called strongly nonlinear) autonomous Hamiltonian differentiable perturbations of the mKdV equation. The proof is based on a weak version of the Birkhoff normal form algorithm and a nonlinear Nash–Moser iteration. The analysis of the linearized operators at each step of the iteration is achieved by pseudo-differential operator techniques and a linear KAM reducibility scheme.File | Dimensione | Formato | |
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