Quasi-periodic solutions in a nonlinear Schrodinger equation

In this paper, one-dimensional (1D) nonlinear Schrodinger equation iu(t) - u(xx) + mu + vertical bar u vertical bar(4)u = 0 with the periodic boundary condition is considered. It is proved that for each given constant potential m and each prescribed integer N > 1, the equation admits a Whitney smooth family of small amplitude, time quasi-periodic solutions with N Diophantine frequencies. The proof is based on a partial Birkhoff normal form reduction and an improved KAM method. (c) 2006 Elsevier Inc. All rights reserved.