On Conditionally Invariant Solutions of Magnetohydrodynamic Equations

TL;DR

This paper develops a conditional symmetry method to find multiple wave solutions of magnetohydrodynamic equations using Riemann invariants, and compares it with the generalized method of characteristics.

Contribution

It introduces a new approach using abelian distributions of vector fields for solving MHD equations under differential constraints.

Findings

Constructed simple and double wave solutions of MHD equations.

Demonstrated the effectiveness of the conditional symmetry method.

Compared the method with the generalized method of characteristics.

Abstract

We present a version of the conditional symmetry method in order to obtain multiple wave solutions expressed in terms of Riemann invariants. We construct an abelian distribution of vector fields which are symmetries of the original system of PDEs subjected to certain first order differential constraints. The usefulness of our approach is demonstrated on simple and double wave solutions of MHD equations. The paper also contains a comparison of the conditional symmetry method with the generalized method of characteristics. Received 19 April, 2003; Accepted 10 June, 2003 Final Version published in J. Nonlinear Math. Phys. 11,1 47-74, (2004).