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.
Yi Wang. Jie Rui. "Quasi-periodic Solutions of Wave Equations with the Nonlinear Term Depending on the Time and Space Variables." Taiwanese J. Math. 24 (3) 629 - 661, June, 2020. https://doi.org/10.11650/tjm/190702