Taiwanese Journal of Mathematics

Quasi-periodic Solutions of Wave Equations with the Nonlinear Term Depending on the Time and Space Variables

Yi Wang and Jie Rui

Full-text: Open access

Abstract

This article is devoted to the study of a wave equation with a constant potential and an $x$-periodic and $t$-quasi-periodic nonlinear term subject to periodic boundary conditions. It is proved that the equation admits small amplitude, linear stable and $t$-quasi-periodic solutions for any constant potential and most frequency vectors.

Article information

Source
Taiwanese J. Math., Volume 24, Number 3 (2020), 629-661.

Dates
Received: 8 August 2018
Revised: 28 May 2019
Accepted: 30 June 2019
First available in Project Euclid: 19 May 2020

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1589875222

Digital Object Identifier
doi:10.11650/tjm/190702

Subjects
Primary: 70K43: Quasi-periodic motions and invariant tori 70K45: Normal forms 70K40: Forced motions 37K55: Perturbations, KAM for infinite-dimensional systems

Keywords
quasi-periodic solutions normal form quasi-periodically forced nonlinear wave equation $x$-dependent term KAM for infinite-dimensional systems

Citation

Wang, Yi; Rui, Jie. Quasi-periodic Solutions of Wave Equations with the Nonlinear Term Depending on the Time and Space Variables. Taiwanese J. Math. 24 (2020), no. 3, 629--661. doi:10.11650/tjm/190702. https://projecteuclid.org/euclid.twjm/1589875222


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