Quasi-periodic solutions for nonlinear wave equation with Liouvillean frequency
type: Item
instance of: scholarly article
title: Quasi-periodic solutions for nonlinear wave equation with Liouvillean frequency
zbMATH Open document ID: 1486.35373
author: Yanling Shi
author: Junxiang Xu
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2021-06-17T00:00:00Z
review text: The authors show that under certain conditions the equation \(u_{tt}-u_{xx}+m u+\epsilon f(\omega t,x,u;\xi)=0\), with Dirichlet boundary conditions, has \(C^\infty\) smooth quasi-periodic solutions. The main result is Theorem 1, whose demonstration is given in section 3.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 37K55
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 7360588
zbMATH Keywords: wave equation
zbMATH Keywords: Liouvillean frequency
zbMATH Keywords: quasi-periodic solution
zbMATH Keywords: infinite dimensional KAM theory
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: fractional Schrödinger equation system
zbMATH Keywords: Töplitz-Lipschitz property
zbMATH Keywords: normal form
MaRDI profile type: Publication
full work available at URL: dcdsb.2020241
OpenAlex ID: W3081333125
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DOI: 10.3934/DCDSB.2020241
description: scientific article; zbMATH DE number 7360588