On Conditionally Invariant Solutions of Magnetohydrodynamic Equations

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).