In this paper, we construct small amplitude quasi-periodic solutions
for one dimensional nonlinear Schrödinger equation
i$u_t=u_{x x}-mu-f(\beta t,x)|u|^2 u,$
with the boundary conditions
$u(t,0)=u(t,a\pi)=0, \ -\infty < t < \infty,$
where $m$ is real and $f(\beta
t,x)$ is real analytic and quasi-periodic on $t$ satisfying the
non-degeneracy condition
$\lim_{T\rightarrow\infty}\frac{1}{T}\int_0^Tf(\beta
t,x)dt\equiv f_0=$ const., $\quad 0\ne f_0 \in\mathbb R,$
with $\beta\in\mathbb R^b$ a fixed Diophantine vector.
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