The Pinney equation and its discretization

Journal of Physics A: Mathematical and General

Volumn 29, Issue 19, 1996, Pages 6343-6352

  Common, A K ^a   Hessameddini, E ^a   Musette, M ^b  

^a UNIVERSITY OF KENT   (United Kingdom)

^b VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030518648     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/29/19/018     Document Type: Article

References (16)

1. Anderson R L, Hamad J and Winternitz P 1982 Systems of ordinary differential equations with non-linear superposition principles Physica 4D 164-82
2. Athorne C 1992 Stability and periodicity in coupled Pinney equations J. Diff. Eqns 100 82-94
3. Athorne C, Rogers C, Ramgulam U and Osbaldestin A 1990 On linearization of the Ermakov system Phys. Lett. 143A 207-12
4. Bountis T C, Papageorgiou V and Winternitz P 1986 The integrability of systems of nonlinear ordinary differential equations with superposition principles J. Math. Phys. 27 1215-24
5. Conte R 1989 Invariant Painlevé analysis of partial differential equations Phys. Lett. 140A 383-90
6. _1992 Unification of PDE and ODE versions of Painlevé analysis into a single invariant version Painlevé Transcendants ed D Levi and P Winternitz (New York: Plenum)
7. Ermakov V P 1880 Second order differential equations. Conditions of complete integrability Univ. Izv. Kiev Series III 9 1-25
8. Faddeev L D and Takhtajan L A 1986 Liouville model on the lattice Springer Lect. Notes Phys. 246 166-79
9. Gambier B 1910 Sur les Équations différentielles du second ordre et du premier degré dont l'intégrable générale est à points critiques fixes Acta Math. 33 1-55
10. Govinder K S and Leach P G L 1994 Ermakov systems: a group theoretical approach Phys. Lett. 186A 391-5
11. Hille E 1976 Ordinary Differential Equations in the Complex Domain (New York: Wiley)
12. Painlevé P 1897 Leçons sur la théorie analytique des équations différentielles Leçons de Stockholm 1895 (Paris: Hermann) reprinted 1972 Oeuvres de Paul Painlevé Editions du CNRS vol 1 (Paris: CNRS)
13. Painlevé P 1897 Leçons sur la théorie analytique des équations différentielles Leçons de Stockholm 1895 (Paris: Hermann) reprinted 1972 Oeuvres de Paul Painlevé Editions du CNRS vol 1 (Paris: CNRS)
14. -3(x) = 0 Proc. Am. Math. Soc. 1 681
15. Ray J R and Reid J L 1979 More exact invariants for the time-dependent harmonic oscillator Phys. Lett. 71A 317-18
16. Rogers C 1989 On a Ermakov system in two-layer long wave theory Research Report Department of Mathematical Sciences, Loughborough University of Technology