Dirac-Lie systems and Schwarzian equations
type: Item
instance of: scholarly article
title: Dirac-Lie systems and Schwarzian equations
zbMATH Open document ID: 1302.34011
author: C. Sardón
author: J. F. Cariñena
author: J. Grabowski
author: J. de Lucas
published in: Journal of Differential Equations
publication date: 2014-07-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1305.6276
review text: In this interesting work, the authors develop a new type of Lie systems on Dirac manifolds that enlarges the notion of Lie-Hamilton systems. Their main geometrical features are analyzed in detail, and their potential use in the analysis of different systems like the SKdV is shown. The main interest, however, is the possibility of studying systems that are not covered by the usual techniques. In particular, criteria for bi-Dirac systems are developed, allowing to deduce the constants of the motion and superposition rules, among other properties. Prospective generalizations of the method to cover other types of systems are discussed.
Mathematics Subject Classification ID: 34A26
Mathematics Subject Classification ID: 17B81
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 6315926
zbMATH Keywords: Dirac structure
zbMATH Keywords: Lie system
zbMATH Keywords: Poisson structure
zbMATH Keywords: Schwarzian equation
zbMATH Keywords: superposition rule
zbMATH Keywords: Vessiot-Guldberg Lie algebra
reviewed by: Rutwig Campoamor Stursberg
MaRDI profile type: Publication
OpenAlex ID: W2092593966
arXiv ID: 1305.6276
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Dirac-Lie systems and Schwarzian equations (DOI)
DOI: 10.1016/J.JDE.2014.05.040