Lower dimensional invariant tori with prescribed frequency for nonlinear wave equation

DOI10.1016/j.jde.2010.04.003zbMath1206.35024OpenAlexW2081438271MaRDI QIDQ603720

Jiansheng Geng, Xiu-Fang Ren

Publication date: 8 November 2010

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2010.04.003

zbMATH Keywords

wave equationBirkhoff normal formKAM theoryHamiltonian systeminvariant torismall-amplitude quasi-periodic solutiontangential frequencies mapping

Mathematics Subject Classification ID

Almost and pseudo-almost periodic solutions to PDEs (35B15) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Second-order semilinear hyperbolic equations (35L71)

Related Items (13)

Quasi-periodic solutions for a Schrödinger equation under periodic boundary conditions with given potential ⋮ Response solutions to harmonic oscillators beyond multi-dimensional Brjuno frequency ⋮ Quasi-periodic solutions of wave equations with the nonlinear term depending on the time and space variables ⋮ Branching of Cantor manifolds of elliptic tori and applications to PDEs ⋮ Quasi-periodic solutions for beam equations with the nonlinear terms depending on the space variable ⋮ Quasiperiodic solutions of completely resonant wave equations with quasiperiodic forced terms ⋮ Quasi-periodic solutions with prescribed frequency in reversible systems ⋮ On reducibility of 1d wave equation with quasiperiodic in time potentials ⋮ Lower dimensional invariant tori with prescribed frequency for the nonlinear Schrödinger equation ⋮ Quasi-periodic solutions for nonlinear wave equation with Liouvillean frequency ⋮ Quasi-Periodic Solutions of Nonlinear Wave Equation with x-Dependent Coefficients ⋮ Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies ⋮ Quasiperiodic solutions of NLS with Liouvillean frequencies

Cites Work

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• Quasi-periodic solutions for a nonlinear wave equation
• Persistence of lower dimensional tori of general types in Hamiltonian systems
• KAM tori for higher dimensional beam equations with constant potentials^*
• Quasi-Periodic Solutions for 1D Schrödinger Equations with Higher Order Nonlinearity

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