### Abstract

The rational solutions for the discrete Painlevé II equation are constructed based on the bilinear formalism. It is shown that they are expressed by a determinant whose entries are given by the Laguerre polynomials. The continuous limit to the Devisme polynomial representation of the rational solutions for the Painlevé II equation is also discussed.

Original language | English |
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Pages (from-to) | 189-199 |

Number of pages | 11 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 232 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - Jul 28 1997 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*232*(3-4), 189-199. https://doi.org/10.1016/S0375-9601(97)00397-6

**Rational solutions for the discrete Painlevé II equation.** / Kajiwara, Kenji; Yamamoto, Kazushi; Ohta, Yasuhiro.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 232, no. 3-4, pp. 189-199. https://doi.org/10.1016/S0375-9601(97)00397-6

}

TY - JOUR

T1 - Rational solutions for the discrete Painlevé II equation

AU - Kajiwara, Kenji

AU - Yamamoto, Kazushi

AU - Ohta, Yasuhiro

PY - 1997/7/28

Y1 - 1997/7/28

N2 - The rational solutions for the discrete Painlevé II equation are constructed based on the bilinear formalism. It is shown that they are expressed by a determinant whose entries are given by the Laguerre polynomials. The continuous limit to the Devisme polynomial representation of the rational solutions for the Painlevé II equation is also discussed.

AB - The rational solutions for the discrete Painlevé II equation are constructed based on the bilinear formalism. It is shown that they are expressed by a determinant whose entries are given by the Laguerre polynomials. The continuous limit to the Devisme polynomial representation of the rational solutions for the Painlevé II equation is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=0040128633&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040128633&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(97)00397-6

DO - 10.1016/S0375-9601(97)00397-6

M3 - Article

VL - 232

SP - 189

EP - 199

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 3-4

ER -