The effects of symmetry-breaking functions on the Ermakov-Pinney equation-Reference-Cited by-同舟云学术

The effects of symmetry-breaking functions on the Ermakov-Pinney equation

Published:2017 Issue:1 Volume:11 Page:62-73
ISSN:1452-8630
Container-title:Applicable Analysis and Discrete Mathematics
language:en
Short-container-title:APPL ANAL DISCRETE M

Author:

Morris R.M.¹,Leach P.G.L.²

Affiliation:

1. Durban University of Technology, Department of Mathematics, Durban, South Africa

2. Durban University of Technology, Institute of Systems Science and Department of Mathematics Durban, South Africa + University of KwaZulu-Natal, School of Mathematics, Statistics and Computer Science, Durban, South Africa

Abstract

The Ermakov-Pinney Equation, x?? + ?2x = h2/x3, has a varied provenance which we briefly delineate. We introduce time-dependent functions in place of the ?2 and h2. The former has no effect upon the algebra of the Lie point symmetries of the equation. The latter destroys the sl(2,R) symmetry and a single symmetry persists only when there is a specific relationship between the two time-dependent functions introduced. We calculate the form of the corresponding autonomous equation for these cases.

Publisher

National Library of Serbia

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

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