A hidden symmetry of the magnetohydrodynamical equations and invariant solutions

Authors

  • A.V. Babich

DOI:

https://doi.org/10.15407/dopovidi2014.02.072

Keywords:

invariant solutions, magnetohydrodynamics, symmetry

Abstract

The group structure of the magnetohydrodynamical equations is considered. Some classes of invariant solutions are constructed with help of the hidden conformal symmetry. The corresponding flows are studied.

Downloads

Download data is not yet available.

References

Polyakov A. M. Calibration fields and strings. Izhevsk: Izd. Udmurtskogo un-ta, 1999 (in Russian).

Landau L. D., Livshyts E. M. Statistical physics. Pt. 1, 5th ed. Moscow: Fizmatlit, 2005 (in Russian).

Belavin A. A., Polyakov A. M., Zamolodchikov A. B. Nucl. Phys. B, 1984, 241(2): 333–380. https://doi.org/10.1016/0550-3213(84)90052-X

Pankratov O. A. Usp. fiz. nauki, 1987, 152: 720–721 (in Russian).

Shykin V. B. Usp. fiz. nauki, 1989, 159: 185-187 (in Russian).

Landau L. D., Livshyts E. M. Electrodynamics of Continuous Media. Moscow: Nauka, 1982 (in Russian).

Ovsyannikov L. V. Lectures on the fundamentals of gas dynamics. Moscow; Izhevsk: Institute of Computer Studies, 2003 (in Russian).

Ibragimov N. Ch. Groups of transformations in mathematical physics. Moscow: Nauka, 1983 (in Russian).

Babich A. V., Klepikov V. F., Shchelkovsky P. A. Visn. Kharkiv. nac. un-tu. Ser. fizychna., 2001, 541, Iss. 4: 68–72 (in Russian).

Dyakonov M., Shur M. Phys. Rev. Lett., 1993, 71: 2465–2468. https://doi.org/10.1103/PhysRevLett.71.2465

Published

27.03.2025

How to Cite

Babich, A. (2025). A hidden symmetry of the magnetohydrodynamical equations and invariant solutions . Reports of the National Academy of Sciences of Ukraine, (2), 72–78. https://doi.org/10.15407/dopovidi2014.02.072