{
  "id": "math-ph/0505028",
  "version": "v1",
  "published": "2005-05-10T10:39:40.000Z",
  "updated": "2005-05-10T10:39:40.000Z",
  "title": "Two important examples of nonlinear oscillators",
  "authors": [
    "José F. Cariñena",
    "Manuel F. Rañada",
    "Mariano Santander"
  ],
  "journal": "Proceedings of 10th International Conference in MOdern GRoup ANalysis (Larnaca, Cyprus, 2004), 39-46",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. This oscillator can be seen as a position-dependent mass system and we show a natural quantization prescription admitting a factorization with shape invariance for the $n=1$ case, and then the energy spectrum is found. Other isochronous systems which can also be considered as a generalization of the harmonic oscillator and admit a nonstandard Lagrangian description are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-10T10:39:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J35"
    ],
    "keywords": [
      "important examples",
      "nonstandard lagrangian description",
      "position-dependent mass system",
      "hyperbolic functions",
      "classical nonlinear oscillator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.ph...5028C"
    }
  }
}