We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear (also called strongly nonlinear) autonomous Hamil- tonian 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. © 2016 Unione Matematica Italiana.

KAM for autonomous quasi-linear perturbations of mKdV / Baldi, P.; 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

Berti, Massimiliano;Montalto, Riccardo
2016-01-01

Abstract

We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear (also called strongly nonlinear) autonomous Hamil- tonian 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. © 2016 Unione Matematica Italiana.
2016
9
2
143
188
https://arxiv.org/abs/1508.02007
http://cdsads.u-strasbg.fr/abs/2016AIHPC..33.1589B
Baldi, P.; Berti, Massimiliano; Montalto, Riccardo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11776
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