THE ALGEBRAIC STRUCTURE OF THE FIRST INTEGRALS OF 3RD-ORDER LINEAR-EQUATIONS

Authors
GOVINDER KS LEACH PGL
Citation
Ks. Govinder et Pgl. Leach, THE ALGEBRAIC STRUCTURE OF THE FIRST INTEGRALS OF 3RD-ORDER LINEAR-EQUATIONS, Journal of mathematical analysis and applications, 193(1), 1995, pp. 114-133
Citations number
9
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics,Mathematics
Journal title
Journal of mathematical analysis and applications → ACNP
ISSN journal
0022247X
Volume
193
Issue
1
Year of publication
1995
Pages
114 - 133
Database
ISI
SICI code
0022-247X(1995)193:1<114:TASOTF>2.0.ZU;2-T
Abstract
We use the Lie theory of extended groups to analyse the first integral s of scalar third-order linear ordinary differential equations. The an alysis reveals three natural classes for which the equation has four, five, or seven symmetries. We show that each class has first integrals with a specific number of symmetries. Illustrative examples of each c lass are given. Comparison is made with the integrals of nonlinear equ ations. (C) 1995 Academic Press, Inc.