Quasi-periodic solutions of nonlinear wave equations with quasi-periodic forcing

DOI10.1016/j.physd.2009.09.003zbMath1183.37122OpenAlexW2098027769MaRDI QIDQ1045860

Min Zhang, Jian-guo Si

Publication date: 16 December 2009

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2009.09.003

zbMATH Keywords

quasi-periodic solutionsinvariant torusinfinite dimensional Hamiltonian systemsKolmogorov-Arnold-Moser (KAM) theoryquasi-periodically forced nonlinear wave equations

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Wave equation (35L05) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

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Cites Work

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• Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum
• Quasi-periodic solutions of completely resonant nonlinear wave equations
• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
• Elements of a qualitative theory of Hamiltonian PDEs
• Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
• Periodic solutions of the equation \(u_{tt}-u_{xx}+u^ 3=0\)
• The nonlinear Klein-Gordon equation on an interval as a perturbed sine-Gordon equation
• Construction of periodic solutions of nonlinear wave equations in higher dimension
• Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
• Quasi-periodic solutions for a nonlinear wave equation
• Time periodic solutions of nonlinear wave equations
• Forced Vibrations of a Nonhomogeneous String
• Periodic solutions of nonlinear vibrating strings and duality principles
• PERTURBATION OF QUASIPERIODIC SOLUTIONS OF INFINITE-DIMENSIONAL HAMILTONIAN SYSTEMS
• Newton's method and periodic solutions of nonlinear wave equations
• Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)
• Quasi-Periodic Solutions of Completely Resonant Forced Wave Equations
• Periodic Solutions of Nonlinear Hyperbolie Partial Differential Equations
• Families of periodic solutions of resonant PDEs
• Time quasi-periodic unbounded perturbations of Schrödinger operators and KAM methods

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