Jacobi's Last Multiplier and the Complete Symmetry Group of the Ermakov-Pinney Equation

DOI

10.2991/jnmp.2005.12.2.10How to use a DOI?

Abstract

The Ermakov-Pinney equation possesses three Lie point symmetries with the algebra sl(2, R). This algebra does not provide a representation of the complete symmetry group of the Ermakov-Pinney equation. We show how the representation of the group can be obtained with the use of the method described in Nucci, J. Nonlin. Math. Phys. 12 (2005) (this issue), which is based on the properties of Jacobi's last mutiplier (Bianchi L, Lezioni sulla teoria dei gruppi continui finiti di trasformazioni, Enrico Spoerri, Pisa, 1918), the method of reduction of order (Nucci,J. Math. Phys 37 (1996), 1772­1775) and an interactive code for calculating symmetries (Nucci, Iteractive REDUCE programs for calcuating classical, non-classical and Lie-Bäcklund symmetries for differential equations (preprint: Georgia Institute of Technology, Math 062090-051, 1990, and CRC Handbook of Lie Group Analysis of Differential Equtions. Vol. 3: New Trends in Theoretical Developments and Computational Methods, Editor: Ibragimov N H, CRC Press, Boca Raton, 1996, 415­481).

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - M.C. Nucci
AU  - P.G.L. Leach
PY  - 2005
DA  - 2005/05/01
TI  - Jacobi's Last Multiplier and the Complete Symmetry Group of the Ermakov-Pinney Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 305
EP  - 320
VL  - 12
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.2.10
DO  - 10.2991/jnmp.2005.12.2.10
ID  - Nucci2005
ER  -