We investigate the initial value problem for a semi-linear Schrödinger equation with exponential-growth nonlinearity. We establish global well-posedness and scattering in the energy space.
"Global well-posedness and scattering of a 2D Schrödinger equation with exponential growth." Bull. Belg. Math. Soc. Simon Stevin 17 (3) 441 - 462, august 2010. https://doi.org/10.36045/bbms/1284570731