Invariant tori of nonlinear Schrodinger equation

In this paper, we consider one-dimensional nonlinear Schrodinger equation iu(t) - u(xx) + V(x)u + f(|u|(2))u = 0 on [0, pi] x R under lthe boundary conditions a(1)u(t, 0) - b(1)u(x)(t, 0) = 0, a(2)u(t, pi) + b(2)u(x)(t, pi) = 0, a(i)(2) + b(i)(2) not equal 0, for i = 1, 2. It is proved that for a prescribed and analytic positive potential V(x), the above equation admits small-amplitude quasi-periodic solutions corresponding to d-dimensional invariant tori of the associated infinite-dimensional dynamical system. (C) 2009 Elsevier Inc. All rights reserved.