### Abstract

We present a class of solutions to the discrete Painleve-II equation for particular values of its parameters. It is shown that these solutions can be expressed in terms of Casorati determinants whose entries are discrete Airy functions. The analogy between the tau function for the discrete P_{II} and that of the discrete Toda molecule equation is pointed out.

Original language | English |
---|---|

Article number | 030 |

Pages (from-to) | 915-922 |

Number of pages | 8 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 27 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 1 1994 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and General*,

*27*(3), 915-922. [030]. https://doi.org/10.1088/0305-4470/27/3/030

**Casorati determinant solutions for the discrete Painleve-II equation.** / Kajiwara, K.; Ohta, Y.; Satsuma, J.; Grammaticos, B.; Ramani, A.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 27, no. 3, 030, pp. 915-922. https://doi.org/10.1088/0305-4470/27/3/030

}

TY - JOUR

T1 - Casorati determinant solutions for the discrete Painleve-II equation

AU - Kajiwara, K.

AU - Ohta, Y.

AU - Satsuma, J.

AU - Grammaticos, B.

AU - Ramani, A.

PY - 1994/12/1

Y1 - 1994/12/1

N2 - We present a class of solutions to the discrete Painleve-II equation for particular values of its parameters. It is shown that these solutions can be expressed in terms of Casorati determinants whose entries are discrete Airy functions. The analogy between the tau function for the discrete PII and that of the discrete Toda molecule equation is pointed out.

AB - We present a class of solutions to the discrete Painleve-II equation for particular values of its parameters. It is shown that these solutions can be expressed in terms of Casorati determinants whose entries are discrete Airy functions. The analogy between the tau function for the discrete PII and that of the discrete Toda molecule equation is pointed out.

UR - http://www.scopus.com/inward/record.url?scp=21344482377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344482377&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/27/3/030

DO - 10.1088/0305-4470/27/3/030

M3 - Article

AN - SCOPUS:21344482377

VL - 27

SP - 915

EP - 922

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 3

M1 - 030

ER -