Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

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

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Integration of Differential Equations by Using Invariants of Discrete Transformation

Author(s):

Zilya Nailevna Khakimova

Mozhaisky Military Space Academy
Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Mathematics

vka@mil.ru

Ajkanush Ashotovna Atojan

Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Mathematics
Mozhaisky Military Space Academy

vka@mil.ru

Abstract:

Ordinary differential equations of the 2nd and 3rd orders with multiplicative right-hand sides of the 2nd and 3rd orders are studied. A method is considered for reducing the order of equations and obtaining exact solutions of differential equations using transformations that are invariants of generators of cyclic transformations discrete groups closed in the classes of differential equations under consideration. The method of discrete invariants is an alternative to the method of "multiplication" of integrable cases in the class of differential equations under study by using the constructed discrete group of transformations acting in this class of equations. Examples are given to illustrate the method of discrete invariants.

Keywords

References:

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