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

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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

Taiwanese J. Math., Advance publication (2019), 33 pages.

First available in Project Euclid: 12 July 2019

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Digital Object Identifier

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

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


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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