# A 2D Schrodinger equation with time-oscillating exponential nonlinearity

## TL;DR

This paper studies the 2D Schrödinger equation with a time-oscillating exponential nonlinearity and proves that solutions converge to a limit as the oscillation frequency increases, with the limit involving the average of the oscillating function.

## Contribution

It establishes the convergence of solutions for a class of initial data in the high-frequency limit of the time-oscillating nonlinearity.

## Key findings

- Solutions converge to a limiting equation as oscillation frequency increases
- The limiting nonlinearity involves the average of the oscillating function
- Convergence holds for initial data in H^1(1d)

## Abstract

This paper deals with the 2-D Schr\"odinger equation with time-oscillating exponential nonlinearity $i\partial_t u+\Delta u= \theta(\omega t)\big(e^{4\pi|u|^2}-1\big)$, 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 $i\partial_t U+\Delta U= I(\theta)\big(e^{4\pi|U|^2}-1\big)$ with the same initial data, where $I(\theta)$ is the average of $\theta$.