Clarkson, Peter
(2003)
*
Remarks on the Yablonskii–Vorob'ev polynomials.
*
Physics Letters A,
319
(1-2).
pp. 137-144.
ISSN 0375-9601.
(doi:10.1016/j.physleta.2003.10.016)
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Official URL http://dx.doi.org/10.1016/j.physleta.2003.10.016 |

## Abstract

It is well known that rational solutions of the second Painlevé equation (PII) are expressed in terms of logarithmic derivatives of the Yablonskii–Vorob'ev polynomials Qn(z) which are defined through a second order, bilinear differential-difference equation which is equivalent to the Toda equation. In this Letter, using the Hamiltonian theory for PII, it is shown that Qn(z) also satisfies a fourth order, bilinear ordinary differential equation and a fifth order, quad-linear difference equation. Further, rational solutions of some ordinary differential equations which are solvable in terms of solutions of PII are also expressed in terms of the Yablonskii–Vorob'ev polynomials.

Item Type: | Article |
---|---|

DOI/Identification number: | 10.1016/j.physleta.2003.10.016 |

Uncontrolled keywords: | painleve equations; Yablonskii-Vorob'ev polynomials |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics |

Depositing User: | Peter A Clarkson |

Date Deposited: | 06 Jun 2008 10:40 UTC |

Last Modified: | 01 Aug 2019 10:30 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/3247 (The current URI for this page, for reference purposes) |

Clarkson, Peter: | https://orcid.org/0000-0002-8777-5284 |

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