KAM for autonomous quasi-linear perturbations of mKdV

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.

49 pages. arXiv admin note: substantial text overlap with arXiv:1404.3125

References in corpus (3)

• KAM for autonomous quasi-linear perturbations of mKdV
• Quasi-periodic solutions for fully nonlinear forced reversible Schroedinger equations
• Gravity capillary standing water waves

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