A KAM Theorem for Higher Dimensional Nonlinear Schrodinger Equations

We prove an infinite dimensional KAM theorem. As an application, we use the theorem to study the higher dimensional nonlinear Schrodinger equation iu(t) - delta u + M xi u + f(vertical bar u vertical bar(2))u = 0, t is an element of R, x is an element of T-d with periodic boundary conditions, where is a real Fourier multiplier and is a real analytic function near with . We obtain for the equation a Whitney smooth family of real-analytic small-amplitude linearly-stable quasi-periodic solutions with a nice linear normal form.