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arXiv · 1508.02007

KAM for autonomous quasi-linear perturbations of mKdV

Pietro Baldi·Massimiliano Berti·Riccardo Montalto
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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.

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Pietro Baldi, Massimiliano Berti, Riccardo Montalto. 2015-08-09. KAM for autonomous quasi-linear perturbations of mKdV. https://doi.org/10.1016/j.anihpc.2015.07.003

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