  We prove existence and uniqueness of smooth solutions with large initial data
for a system of equations modeling the interaction of short waves, governed by
a nonlinear Schr\"odinger equation, and long waves, described by the equations
of magnetohydrodynamics. In the model, the short waves propagate along the
streamlines of the fluid flow. This is translated in the system by setting up
the nonlinear Schr\"odinger equation in the Lagrangian coordinates of the
fluid. Besides, the equations are coupled by nonlinear terms accounting for the
strong interaction of the dynamics. The system provides a simplified
mathematical model for studying aurora type phenomena. We focus on the
2-dimensional case with periodic boundary conditions. This is the first result
on existence of smooth solutions with large data for the multidimensional case
of the model under consideration.

Analysis of PDEs