SCATTERING IN THE WEIGHTED L2-SPACE FOR A 2D NONLINEAR SCHRODINGER EQUATION WITH INHOMOGENEOUS EXPONENTIAL NONLINEARITY

We investigate the defocusing inhomogeneous nonlinear Schrodinger equation i partial derivative(t)u + Delta u = vertical bar x vertical bar(-b) (e(alpha vertical bar u vertical bar 2) - 1 - alpha vertical bar u vertical bar(2))u, u(0) = u(0), x is an element of R-2, with 0 < b < 1 and alpha = 2 pi(2 - b). First we show the decay of global solutions by assuming that the initial data u(0) belongs to the weighted space Sigma(R-2) ={u is an element of H-1 (R-2) : vertical bar x vertical bar u is an element of L-2 (R-2)}. Then we combine the local theory with the decay estimate to obtain scattering in Sigma when the Hamiltonian is below the value 2/(1+b)(2-b).