Symmetry 2016, 8(3), 15; doi:10.3390/sym8030015
Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations
Instituto
de Matemática Interdisciplinar and Depto. Geometría y Topología,
Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid E-28040,
Spain
Academic Editor: Roman M. Cherniha
Received: 1 December 2015 / Revised: 24 February 2016 / Accepted: 26 February 2016 / Published: 17 March 2016
(This article belongs to the Special Issue Symmetry and Integrability)
View Full-Text
|
Download PDF [254 KB, uploaded 17 March 2016]
Abstract
A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems. View Full-Text
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any
medium, provided the original work is properly cited. (CC BY 4.0).
Scifeed alert for new publications
Never miss any articles matching your research from any publisher- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now
Share & Cite This Article
MDPI and ACS Style
Campoamor-Stursberg, R. Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations. Symmetry 2016, 8, 15.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
Related Articles
Article Metrics
For more information on the journal statistics, click here.
Multiple requests from the same IP address are counted as one view.
Comments
Citations
2
Click to view
Symmetry
EISSN 2073-8994
Published by MDPI AG, Basel, Switzerland
RSS
E-Mail Table of Contents Alert