Abstract
We investigate the initial value problem for a defocusing nonlinear Schrodinger equation with weighted exponential nonlinearity
i partial derivative(t)u +Delta u =u/vertical bar x vertical bar(b)(e(alpha vertical bar u vertical bar 2) -1); (t,x) is an element of R x R-2,
where 0 < b < 1. and alpha = 2 pi(2 - b). We establish local and global well-posedness in the subcritical and critical regimes.