Construction of periodic solutions of nonlinear wave equations with Dirichlet boundary conditions by the Lindstedt series method
type: Item
instance of: scholarly article
title: Construction of periodic solutions of nonlinear wave equations with Dirichlet boundary conditions by the Lindstedt series method
zbMATH Open document ID: 1065.35028
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2004-11-23T00:00:00Z
review text: The existence of periodic solutions is shown for nonlinear wave equations (like the Klein-Gordon and sine-Gordon equations) of the form \(u_{tt}-u_{xx}+\mu u=f(u)\) with Dirichlet boundary value conditions, where \(\mu\) is a positive real number and \(f\) is odd and analytic. A renormalized Lindstedt series is used and renormalized group methods are applied to show their convergence.
reviewed by: Michal Fečkan
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35B20
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 37K55
Mathematics Subject Classification ID: 81T17
zbMATH DE Number: 2118446
zbMATH Keywords: periodic solutions
zbMATH Keywords: wave equations
zbMATH Keywords: Lindstedt series
zbMATH Keywords: Klein-Gordon equation
zbMATH Keywords: sine-Gordon equation
zbMATH Keywords: Dirichlet boundary value conditions
author: Guido Gentile
author: Vieri Mastropietro
MaRDI profile type: Publication
full work available at URL: j.matpur.2004.01.007
OpenAlex ID: W2047157783
cites work: Q4786565
cites work: Q4763964
cites work: Construction of periodic solutions of nonlinear wave equations in higher dimension
cites work: Q4945128
cites work: Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
cites work: Newton's method and periodic solutions of nonlinear wave equations
cites work: Q4378706
cites work: Twistless KAM tori
cites work: Hyperbolic low-dimensional invariant tori and summations of divergent series
cites work: Quasi-periodic solutions for two-level systems
cites work: METHODS FOR THE ANALYSIS OF THE LINDSTEDT SERIES FOR KAM TORI AND RENORMALIZABILITY IN CLASSICAL MECHANICS: A review with Some Applications
cites work: Anderson localization for the Holstein model
cites work: Renormalization group for one-dimensional fermions. A review on mathematical results
cites work: Q5682013
cites work: Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
cites work: Quasi-periodic solutions for a nonlinear wave equation
cites work: Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
cites work: Normal modes for nonlinear Hamiltonian systems
DOI: 10.1016/J.MATPUR.2004.01.007
description: scientific article; zbMATH DE number 2118446