KAM for quasi-linear KdV

DOI10.1016/j.crma.2014.04.012zbMath1302.35331arXiv1404.3125OpenAlexW2040923341MaRDI QIDQ404419

Pietro Baldi, Massimiliano Berti, Riccardo Montalto

Publication date: 4 September 2014

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.3125

zbMATH Keywords

KdVKAM for PDEsquasi-linear PDEs

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

Related Items (18)

Quasi-periodic solutions for the derivative nonlinear Schrödinger equation with finitely differentiable nonlinearities ⋮ KAM for PDEs ⋮ KAM for autonomous quasi-linear perturbations of mKdV ⋮ Smooth quasi-periodic solutions for the perturbed mKdV equation ⋮ KAM tori for defocusing KdV-mKdV equation ⋮ KAM theory for the reversible perturbations of 2D linear beam equations ⋮ Bounded non-response solutions with Liouvillean forced frequencies for nonlinear wave equations ⋮ Quasi-periodic solutions for the reversible derivative nonlinear Schrödinger equations with periodic boundary conditions ⋮ Invariant tori for reversible nonlinear Schrödinger equations under quasi-periodic forcing ⋮ Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves ⋮ Reducibility of 1-d Schrödinger equation with time quasiperiodic unbounded perturbations. I ⋮ KAM tori for completely resonant Hamiltonian derivative beam equations on \(\mathbb{T}^2\) ⋮ On time periodic solutions to the conformal cubic wave equation on the Einstein cylinder ⋮ Invariant tori for a derivative nonlinear Schrödinger equation with quasi-periodic forcing ⋮ Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies ⋮ KAM tori for generalized Benjamin-Ono equation ⋮ A KAM result on compact Lie groups ⋮ Gravity capillary standing water waves

Cites Work

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• KAM for autonomous quasi-linear perturbations of mKdV
• A KAM theorem for Hamiltonian partial differential equations with unbounded perturbations
• A normal form for the Schrödinger equation with analytic non-linearities
• Quasi-periodic solutions for a nonlinear wave equation
• Periodic solutions of fully nonlinear autonomous equations of Benjamin-Ono type
• Standing waves on an infinitely deep perfect fluid under gravity

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