Symmetries of PDEs Systems in Solar Physics and Contact Geometry

TL;DR

This paper investigates the symmetry groups of specific PDE systems in solar physics, particularly the Blair system, revealing their geometric structures and generating new solutions through symmetry analysis.

Contribution

It identifies the symmetry group of the Blair system and demonstrates how symmetry methods produce both known and new solutions in the context of contact geometry and solar physics.

Findings

The symmetry group of the Blair system is explicitly determined.

Known solutions are shown to be group-invariant.

New solutions are constructed using symmetry group analysis.

Abstract

One considers a special class of PDEs systems and one determines the associated symmetry group. Particulary, for the Blair system, one finds the symmetry group. A solutions of the Blair system gives a conformally flat contact metric structure and also it defines a "force-free" model of solar physics. By using the symmetry groups theory, one shows that the known solutions are group-invariant solutions and one gives new solutions.