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Русская версия

**S. Y. Malamanov**

Professor, Baltic State Technical University,

St. Petersburg, Russia.

In this paper, we consider the factor system of the equations of magnetohydrodynamics, a system of differential equations that relates only invariants (finite functional basis of invariants) to the subgroup of the basic group admissible in the system under consideration. We consider invariant solutions with respect to the extension operator, and the initial system of equations is essentially simplified. Such solutions are most typical for problems arising in the modeling of physical processes. Possible ways of simplifying the formulation of problems are indicated. Classical group analysis is applied to the factorized system of equations of marine electrodynamics in the case of a constant external magnetic field. Knowledge of the allowable group results in finding new solutions. The Lie subalgebra of operators and the corresponding transformation group are found. The possibility of decomposition of the system of equations of marine electrodynamics is shown.

- differential equations
- magnetic field
- marine electrodynamics
- reduction of order
- transformation groups

- Malamanov S. YU. Faktorizatsiya uravneniy morskoy elektrodinamiki [Factorization of the equations of marine electrodynamics] // Differentsial'nyye uravneniya i protsessy upravleniya. № 3, 2017. - p. 37-45. available at: http://diffjournal.spbu.ru/pdf/malamanov5.pdf
- Ovsyannikov L. V. Gruppovoy analiz differentsial'nykh uravneniy [Group analysis of differential equations]. -M. : Nauka, 1978. - 400 s
- Savchenko V. N., Smagin V. P., Fonarev G. A. Voprosy morskoy elektrodinamiki [Questions of marine electrodynamics: Monografiya. - Vladivostok: Izd-vo VGUE i S, 1999. - 208 s