A 2D Schrodinger equation with time-oscillating exponential nonlinearity

This paper deals with the 2-D Schrodinger equation with time-oscillating exponential nonlinearity $ipartial_t u+Delta u= theta(omega t)big(e^{4pi|u|^2}-1big)$, where $theta$ is a periodic $C^1$-function. We prove that for a class of initial data $u_0 in H^1(mathbb{R}^2)$, the solution $u_{omega}$ converges, as $|omega|$ tends to infinity to the solution $U$ of the limiting equation $ipartial_t U+Delta U= I(theta)big(e^{4pi|U|^2}-1big)$ with the same initial data, where $I(theta)$ is the average of $theta$.