Gupta, Hari Shanker and Prasad, Phoolan
(2011)
*A bicharacteristic formulation of the ideal MHD equations.*
In: Journal of Plasma Physics, 77
(Part 2).
pp. 169-191.

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## Abstract

On a characteristic surface Omega of a hyperbolic system of first-order equations in multi-dimensions (x, t), there exits a compatibility condition which is in the form of a transport equation along a bicharacteristic on Omega. This result can be interpreted also as a transport equation along rays of the wavefront Omega(t) in x-space associated with Omega. For a system of quasi-linear equations, the ray equations (which has two distinct parts) and the transport equation form a coupled system of underdetermined equations. As an example of this bicharacteristic formulation, we consider two-dimensional unsteady flow of an ideal magnetohydrodynamics gas with a plane aligned magnetic field. For any mode of propagation in this two-dimensional flow, there are three ray equations: two for the spatial coordinates x and y and one for the ray diffraction. In spite of little longer calculations, the final four equations (three ray equations and one transport equation) for the fast magneto-acoustic wave are simple and elegant and cannot be derived in these simple forms by use of a computer program like REDUCE.

Item Type: | Journal Article |
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Additional Information: | Copyright of this article belongs to Cambridge University Press. |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 07 Apr 2011 06:01 |

Last Modified: | 26 May 2011 10:33 |

URI: | http://eprints.iisc.ernet.in/id/eprint/36003 |

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