In this paper, one dimensional nonlinear wave equation
$ u_{tt}-u_{xx} +mu +\varepsilon f(\omega t,x,u;\xi) = 0 $
with Dirichlet boundary condition is considered, where $ \varepsilon $ is small positive parameter, $ \omega = \xi \bar{\omega}, $ $ \bar{\omega} $ is weak Liouvillean frequency. It is proved that there are many quasi-periodic solutions with Liouvillean frequency for the above equation. The proof is based on an infinite dimensional KAM Theorem.
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