Superposition rules for higher-order systems and their applications
Mathematical Physics
2012-04-27 v2 Classical Analysis and ODEs
Differential Geometry
math.MP
Abstract
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this notion and other related ones to systems of higher-order differential equations and analyse their properties. Several results concerning the existence of various types of superposition rules for higher-order systems are proved and illustrated with examples extracted from the physics and mathematics literature. In particular, two new superposition rules for second- and third-order Kummer--Schwarz equations are derived.
Cite
@article{arxiv.1111.4070,
title = {Superposition rules for higher-order systems and their applications},
author = {J. F. Cariñena and J. Grabowski and J. de Lucas},
journal= {arXiv preprint arXiv:1111.4070},
year = {2012}
}
Comments
(v2) 33 pages, some typos corrected, added some references and minor commentaries