Abstract
We present two partially invariant solutions to ideal magnetohydrodynamics equations. The solutions describe generalizations of the classical one-dimensional fluid motions with planar and spherical waves. In both cases an overdetermined system of determining equations is reduced to involutive system of equations with two independent variables and a finite relation. Clear geometrical interpretation of the finite relation allows describing picture of the flow in the whole 3D space.
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Golovin, S.V. (2008). Partially Invariant Solutions to Ideal Magnetohydrodynamics. In: Eastwood, M., Miller, W. (eds) Symmetries and Overdetermined Systems of Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 144. Springer, New York, NY. https://doi.org/10.1007/978-0-387-73831-4_18
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DOI: https://doi.org/10.1007/978-0-387-73831-4_18
Publisher Name: Springer, New York, NY
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Online ISBN: 978-0-387-73831-4
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