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

Advance publication

This article is in its final form and can be cited using the date of online publication and the DOI.

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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., Advance publication (2019), 33 pages.

Dates
First available in Project Euclid: 12 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1562896821

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., advance publication, 12 July 2019. doi:10.11650/tjm/190702. https://projecteuclid.org/euclid.twjm/1562896821


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