Dimensional reduction of nonlinear differential equations on homogeneous spaces

O. L. Kurnyavko^a, I. V. Shirokov<sup>b

a</sup> Omsk Institute of Water Transport, Omsk, Russia
^b Omsk State Technical University, Omsk, Russia

Abstract: We consider the problem of dimensional reduction of nonlinear differential equations on homogeneous spaces that have no symmetries in general. The proposed method allows passing to a differential equation with fewer independent variables and, in particular, to ordinary differential equations.

Keywords: Lie algebra, Lie group, homogeneous spaces, morphism of homogeneous spaces, reduction.

Received: 27.01.2025
Revised: 05.03.2025

DOI: 10.4213/tmf10897

 English version: Theoretical and Mathematical Physics, 2025, 223:2, 755–769

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