THE CONSTRUCTION OF QUASI-PERIODIC SOLUTIONS OF QUASI-PERIODIC FORCED SCHRODINGER EQUATION

In this paper, we construct small amplitude quasi-periodic solutions for one dimensional nonlinear Schrodinger equation iu(t) = u(xx) - mu - f(beta t, x)vertical bar u vertical bar(2)u with the boundary conditions u(t, 0) = u(t, a pi) = 0, -infinity < t < infinity, where m is real and f(beta t, x) is real analytic and quasi-periodic on t satisfying the non-degeneracy condition lim(T ->infinity) 1/T integral(T)(0) f(beta t, x)dt equivalent to f(0) = const., 0 not equal f(0) is an element of R, with beta is an element of R(b) a fixed Diophantine vector.