Symmetry properties of some Euler-type equations in plasma physics

TL;DR

This paper analyzes the symmetry properties of a plasma physics PDE system, identifying all Lie point symmetries, invariant solutions, and discussing conditional symmetries, while noting the absence of potential symmetries despite conserved currents.

Contribution

It provides a comprehensive Lie symmetry analysis of a plasma physics PDE system, including invariant solutions and symmetry classifications, which was not previously documented.

Findings

All Lie point symmetries of the system are identified.

Invariant solutions corresponding to these symmetries are constructed.

The system admits conserved currents but no potential symmetries.

Abstract

We consider a system of partial differential equations, of interest to plasma physics, and provide all its Lie point symmetries, with their respective invariant solutions. We also discuss some of its conditional and partial symmetries. We finally show that, although the system can be cast in divergence form and admits conserved currents, it does not admit potential symmetries.