Abstract
The problem of the existence of self-similar solutions for astrophysical magnetohydrodynamic (MHD) transient flows is considered. Our approach is based on the pioneering works by B.C. Low for coronal transients and their further generalizations. The axiomatic basis of the approach is adjusted and verified. It is shown that the introduction of a new type of “triple-compound” variable may lead to the appearance of new classes of analytic self-similar solutions, possibly relevant for a number of interesting astrophysical situations. The possibility of the development of a self-similar model for a strongly magnetized plasma with pressure anisotropy is indicated. It is argued that proper changes of the model’s geometric and kinematic features may lead to the discovery of other, more complex and less idealized classes of self-similar solutions.
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