Energy Scattering for Schrodinger Equation with Exponential Nonlinearity in Two Dimensions

When the spatial dimensions n = 2, the initial data u(0) epsilon H-1, and the Hamiltonian H(u(0)) <= 1, we prove that the scattering operator is well defined in the whole energy space H-1(R-2) for nonlinear Schrodinger equation with exponential nonlinearity (e(lambda vertical bar u vertical bar 2) - 1)u, where 0 < lambda < 4 pi.