Construction of periodic solutions of nonlinear wave equations with Dirichlet boundary conditions by the Lindstedt series method

DOI10.1016/j.matpur.2004.01.007zbMath1065.35028OpenAlexW2047157783MaRDI QIDQ1887188

Vieri Mastropietro, Guido Gentile

Publication date: 23 November 2004

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2004.01.007

zbMATH Keywords

periodic solutionsKlein-Gordon equationwave equationssine-Gordon equationLindstedt seriesDirichlet boundary value conditions

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Periodic solutions to PDEs (35B10) Second-order nonlinear hyperbolic equations (35L70) Nonlinear first-order PDEs (35F20) Renormalization group methods applied to problems in quantum field theory (81T17) Perturbations in context of PDEs (35B20) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

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Cites Work

• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
• Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
• Twistless KAM tori
• Quasi-periodic solutions for two-level systems
• Hyperbolic low-dimensional invariant tori and summations of divergent series
• Construction of periodic solutions of nonlinear wave equations with Dirichlet boundary conditions by the Lindstedt series method
• 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
• Normal modes for nonlinear Hamiltonian systems
• Newton's method and periodic solutions of nonlinear wave equations
• METHODS FOR THE ANALYSIS OF THE LINDSTEDT SERIES FOR KAM TORI AND RENORMALIZABILITY IN CLASSICAL MECHANICS: A review with Some Applications
• Anderson localization for the Holstein model
• Renormalization group for one-dimensional fermions. A review on mathematical results
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