This article is cited in 21 papers

Bicentennial of C.G. Jacobi

A nonlinear deformation of the isotonic oscillator and the Smorodinski–Winternitz system: integrability and superintegrability

J. F. Cariñena^a, M. F. Rañada^a, M. Santander<sup>b

a</sup> Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
^b Departamento de Física Teórica, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid, Spain

Abstract: The properties of a nonlinear deformation of the isotonic oscillator are studied. This deformation affects to both the kinetic term and the potential and depends on a parameter $\lambda$ in such a way that for $\lambda=0$ all the characteristics of of the classical system are recovered. In the second part, that is devoted to the two-dimensional case, a $\lambda$-dependent deformation of the Smorodinski–Winternitz system is studied. It is proved that the deformation introduced by the parameter $\lambda$ modifies the Hamilton–Jacobi equation but preserves the existence of a multiple separability.

Keywords: nonlinear equations, nonlinear oscillators, integrability, superintegrability, Hamilton–Jacobi separability.

MSC: 37J35, 34A34, 34C15, 70H06

Received: 24.02.2005
Accepted: 16.05.2005

Language: English

DOI: 10.1070/RD2005v010n04ABEH000324

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