# Symmetries of Reduced Magnetohydrodynamics

## TL;DR

This paper uses Lie-symmetry methods to identify the symmetry group of reduced magnetohydrodynamics, revealing new symmetries and exact solutions, and compares it with a simpler plasma turbulence model.

## Contribution

It introduces a comprehensive symmetry analysis of reduced magnetohydrodynamics, uncovering unexpected symmetries and exact nonlinear solutions not previously documented.

## Key findings

- Identified continuous symmetry group including space-time transformations.
- Discovered unexpected symmetries beyond standard translations and rotations.
- Derived new exact nonlinear solutions for the reduced system.

## Abstract

Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation reveals, in addition to the predictable translation and rotation groups, some unexpected symmetries. It also uncovers novel, exact nonlinear solutions to the reduced system. A similar analysis of a related but simpler system, describing nonlinear plasma turbulence in terms of a single field, is also presented.