Atlantis Press Paper Details: Jacobi's Last Multiplier and the Complete Symmetry Group of the Ermakov-Pinney Equation

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).

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title:		Jacobi's Last Multiplier and the Complete Symmetry Group of the Ermakov-Pinney Equation
publication:		JNMP
volume-issue:		12 - 2
pages:		305 - 320
ISSN:		1402-9251
DOI:		doi:10.2991/jnmp.2005.12.2.10 (how to use a DOI)
author(s):		M C NUCCI, P G L LEACH
publication date:		May 2005
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:		© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
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