Volume 11, Issue 1, February 2004, Pages 47 - 74
On Conditionally Invariant Solutions of Magnetohydrodynamic Equations. Multiple Waves.
A M GRUNDLAND, P PICARD
A M GRUNDLAND
Received 19 April 2003, Accepted 10 June 2003, Available Online 1 February 2004.
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- 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.
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Cite this article
TY - JOUR AU - A M GRUNDLAND AU - P PICARD PY - 2004 DA - 2004/02 TI - On Conditionally Invariant Solutions of Magnetohydrodynamic Equations. Multiple Waves. JO - Journal of Nonlinear Mathematical Physics SP - 47 EP - 74 VL - 11 IS - 1 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2004.11.1.5 DO - https://doi.org/10.2991/jnmp.2004.11.1.5 ID - GRUNDLAND2004 ER -