Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

The Search of the Quotient System for Magnetohydrodynamics Equations

Author(s):

S. Y. Malamanov

Faculty of Applied Mathematics - Control Processes,
doctoral student.
Saint Petersburg State University,
Saint-Petersburg, Russia.
Candidate of Physical and Mathematical Sciences.

stevmal@mail.ru

Abstract:

The paper deals with finding the quotient system of equations of magnetohydrodynamics - the system of differential equations which connects only the invariants (finite functional basis of invariants) of a subgroup of the main group permitted by the system. We consider solutions invariant under the extension operator. Such solutions are most typical for the problems arising in the modeling of physical processes.

Keywords

• differential equations
• invariant solution
• order decreasing
• symmetry group
• the basis of invariants

References:

1. Novozhilov V. V., Pavlovskiy V. A. Ustanovivshiyesya turbulentnyye techeniya neszhimaye-moy zhidkosti [ Steady turbulent flow of an incompressible fluid]. - SPb: SPbGU, 2013. - 483 s
2. Ovsyannikov L. V. Gruppovoy analiz differentsial'nykh uravneniy [Group analysis of differential equations ] -M. : Nauka, 1978. - 400 s

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