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2013
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 Carinena J. F., Ranada M. F., Santander M. A nonlinear deformation of the isotonic oscillator and the Smorodinski–Winternitz system: integrability and superintegrability 2005, vol. 10, no. 4, pp.  423-436 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 Citation: Carinena J. F., Ranada M. F., Santander M.,  A nonlinear deformation of the isotonic oscillator and the Smorodinski–Winternitz system: integrability and superintegrability , Regular and Chaotic Dynamics, 2005, vol. 10, no. 4, pp. 423-436 DOI:10.1070/RD2005v010n04ABEH000324