A note on coupled nonlinear Schrödinger equations - Saanouni Tarek (Advances in Nonlinear Analysis, 2014)
We investigate the initial value problem for some coupled nonlinear Schrödinger equations in two space dimensions with exponential growth. We prove global well-posedness and scattering in the defocusing case. In the focusing sign, existence of non-global solution is discussed via the potential-well theory.