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This article is cited in 21 scientific papers (total 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. Cariñenaa, M. F. Rañadaa, M. Santanderb a 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.
Received: 24.02.2005 Accepted: 16.05.2005
Citation:
J. F. Cariñena, M. F. Rañada, M. Santander, “A nonlinear deformation of the isotonic oscillator and the Smorodinski–Winternitz system: integrability and superintegrability”, Regul. Chaotic Dyn., 10:4 (2005), 423–436
Linking options:
https://www.mathnet.ru/eng/rcd719 https://www.mathnet.ru/eng/rcd/v10/i4/p423
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