A KAM theorem for one dimensional Schrodinger equation with periodic boundary conditions

In this paper, one-dimensional (1 D) nonlinear Schrodinger equation iu(t) - u(xx) + mu + partial derivativeg(u, (u) over bar)/partial derivative(u) over bar = 0, with Periodic Boundary Conditions is considered; m is not an element of (1)/(12)Z is a real parameter and the nonlinearity g(u, (u) over bar) = Sigma(j,l,j+l) a(jl)u(j-l)u, a(jl) = a(lj) is an element of R, a(22) not equal 0 is a real analytic function in a neighborhood of the origin. The KAM machinery is adapted to fit the above equation so as to construct small-amplitude periodic or quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system. (C) 2004 Elsevier Inc. All rights reserved.