Applications of Symmetry Methods to the Theory of Plasma Physics

TL;DR

This paper demonstrates how symmetry methods can be effectively applied to solve and analyze complex PDEs in plasma physics, providing insights into their solutions and classifications.

Contribution

It presents three examples illustrating the application of symmetry techniques to analyze plasma physics PDEs, including symmetry analysis, solutions, and classification.

Findings

Complete symmetry analysis of a system of two PDEs

Construction of group-invariant solutions

Symmetry classification of a nonlinear PDE

Abstract

The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal advantage of this "interaction" between plasma physics and symmetry techniques. The examples include, in particular, the complete symmetry analysis of system of two PDE's, with the determination of some conditional and partial symmetries, the construction of group-invariant solutions, and the symmetry classification of a nonlinear PDE.