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- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266112120099
- Publisher site
- See Article on Publisher Site
Abstract
We consider the problem on the reducibility of control systems to systems whose dependent variables split into two groups, Liouville variables and integral variables. The values and derivatives of Liouville variables are arbitrary, and the integral variables are represented as integrals of functions depending only on the values and derivatives of the Liouville variables. In this connection, we use invertible transformations of the most general form in which the new dependent variables are functions of old variables and their derivatives of arbitrary finite order; moreover, the independent variable can also change. To solve this problem, we use methods of infinite-dimensional geometry, in particular, the earlier-obtained descriptions of higher symmetries for control systems and integrable symmetries of differential equations.
Journal
Differential Equations – Springer Journals
Published: Jan 23, 2013