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

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Regular and Chaotic Dynamics, 2005, Volume 10, Issue 4, Pages 423–436
DOI: https://doi.org/10.1070/RD2005v010n04ABEH000324 (Mi rcd719)

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. Cariñena^a, M. F. Rañada^a, M. Santander^b

^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

Citations (21)

DOI: https://doi.org/10.1070/RD2005v010n04ABEH000324

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

λ

$\lambda$ in such a way that for

λ = 0

$\lambda=0$ all the characteristics of of the classical system are recovered. In the second part, that is devoted to the two-dimensional case, a

λ

$\lambda$ -dependent deformation of the Smorodinski–Winternitz system is studied. It is proved that the deformation introduced by the parameter

λ

$\lambda$ 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

Bibliographic databases:

Document Type: Article

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

Language: English

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

Citation in format AMSBIB

\Bibitem{CarRanSan05}

\by J. F. Cari\~nena, M.~F.~Ra{\~n}ada, M.~Santander

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

\jour Regul. Chaotic Dyn.

\yr 2005

\vol 10

\issue 4

\pages 423--436

\mathnet{http://mi.mathnet.ru/rcd719}

\crossref{https://doi.org/10.1070/RD2005v010n04ABEH000324}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2191371}

\zmath{https://zbmath.org/?q=an:1133.70326}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2005RCD....10..423C}

Linking options:

https://www.mathnet.ru/eng/rcd719

https://www.mathnet.ru/eng/rcd/v10/i4/p423

This publication is cited in the following 21 articles:

V. K. Chandrasekar, R. Gladwin Pradeep, R. Mohanasubha, M. Senthilvelan, M. Lakshmanan, “Method of deriving Lagrangian for two-dimensional systems”, Eur. Phys. J. Plus, 138:1 (2023)
Mustafa O., “N-Dimensional Pdm-Damped Harmonic Oscillators: Linearizability, and Exact Solvability”, Phys. Scr., 96:6 (2021), 065205
Mustafa O., “Isochronous N-Dimensional Nonlinear Pdm-Oscillators: Linearizability, Invariance and Exact Solvability”, Eur. Phys. J. Plus, 136:2 (2021), 249
Mustafa O., “N-Dimensional Pdm Non-Linear Oscillators: Linearizability and Euler-Lagrange Or Newtonian Invariance”, Phys. Scr., 95:6 (2020), 065214
Mustafa O., “Pdm Creation and Annihilation Operators of the Harmonic Oscillators and the Emergence of An Alternative Pdm-Hamiltonian”, Phys. Lett. A, 384:13 (2020), 126265
Mustafa O., Algadhi Z., “Position-Dependent Mass Momentum Operator and Minimal Coupling: Point Canonical Transformation and Isospectrality”, Eur. Phys. J. Plus, 134:5 (2019), 228
Shahram Dehdashti, Ali Mahdifar, Huaping Wang, “Coherent States of Position-Dependent Mass Oscillator”, Int J Theor Phys, 55:8 (2016), 3564
Dibakar Ghosh, Barnana Roy, “Nonlinear dynamics of classical counterpart of the generalized quantum nonlinear oscillator driven by position dependent mass”, Annals of Physics, 353 (2015), 222
Omar Mustafa, “Position-dependent mass Lagrangians: nonlocal transformations, Euler–Lagrange invariance and exact solvability”, J. Phys. A: Math. Theor., 48:22 (2015), 225206
Rami Ahmad El-Nabulsi, “A Generalized Nonlinear Oscillator From Non-Standard Degenerate Lagrangians and Its Consequent Hamiltonian Formalism”, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 84:4 (2014), 563
Manuel F. Rañada, “A quantum quasi-harmonic nonlinear oscillator with an isotonic term”, Journal of Mathematical Physics, 55:8 (2014)
R. Mohanasubha, M.I. Sabiya Shakila, M. Senthilvelan, “On the linearization of isochronous centre of a modified Emden equation with linear external forcing”, Communications in Nonlinear Science and Numerical Simulation, 19:4 (2014), 799
B Midya, B Roy, A Biswas, “Coherent state of a nonlinear oscillator and its revival dynamics”, Phys. Scr., 79:6 (2009), 065003
B Midya, B Roy, “A generalized quantum nonlinear oscillator”, J. Phys. A: Math. Theor., 42:28 (2009), 285301
Vadas Gintautas, Alfred W. Hübler, “Resonant forcing of nonlinear systems of differential equations”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 18:3 (2008)
Á. Ballesteros, A. Enciso, F.J. Herranz, O. Ragnisco, “A maximally superintegrable system on an -dimensional space of nonconstant curvature”, Physica D: Nonlinear Phenomena, 237:4 (2008), 505
J. F. Cariñena, M. F. Rañada, M. Santander, “Quantization of a nonlinear oscillator as a model of the harmonic oscillator on spaces of constant curvature: One- and two-dimensional systems”, Phys. Atom. Nuclei, 71:5 (2008), 836
José F. Cariñena, Manuel F. Rañada, Mariano Santander, “A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog”, SIGMA, 3 (2007), 030, 23 pp.
José F. Cariñena, Manuel F. Rañada, Mariano Santander, “A quantum exactly solvable non-linear oscillator with quasi-harmonic behaviour”, Annals of Physics, 322:2 (2007), 434
J. F. Cariñena, M. F. Rañada, M. Santander, “Three superintegrable two-dimensional oscillators: Superintegrability, nonlinearity, and curvature”, Phys. Atom. Nuclei, 70:3 (2007), 505

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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