ON THE EXISTENCE OF FULL DIMENSIONAL KAM TORUS FOR FRACTIONAL NONLINEAR SCHRODINGER EQUATION

In this paper, we study fractional nonlinear Schrodinger equation (FNLS) with periodic boundary condition iu(t) = -(-Delta)(s0)u - V * u - epsilon f(x)vertical bar u vertical bar(4)u, x is an element of T, t is an element of R, s(0) is an element of (1/2, 1), (0.1) where (-Delta)(s0) is the Riesz fractional differentiation defined in [21] and V* is the Fourier multiplier defined by (V * u) over cap (n) = V-n(u) over cap (n), V-n is an element of [-1, 1], and f(x) is Gevrey smooth. We prove that for 0 <= vertical bar epsilon vertical bar << 1 and appropriate V, the equation (0.1) admits a full dimensional KAM torus in the Gevrey space satisfying 1/2e(-rn theta) <= vertical bar q(n)vertical bar <= 2e(-rn theta), theta is an element of (0, 1), which generalizes the results given by [8-10] to fractional nonlinear Schrodinger equation.