### Abstract

We show that, under certain conditions, some difference Painlevé equations have nontrivial meromorphic solutions in the whole complex plane. These meromorphic solutions are obtained by analytic continuation of asymptotic solutions given in sectors of zero opening angle. The existence of these asymptotic solutions is shown by using fundamental matrix solutions of the associated linear systems with double unit characteristic roots and with coefficients expressed by asymptotic series in fractional powers.

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

Article number | 315213 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 31 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Modelling and Simulation
- Statistics and Probability

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*42*(31), [315213]. https://doi.org/10.1088/1751-8113/42/31/315213

**Meromorphic solutions of difference Painlevé equations.** / Shimomura, Shun.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 42, no. 31, 315213. https://doi.org/10.1088/1751-8113/42/31/315213

}

TY - JOUR

T1 - Meromorphic solutions of difference Painlevé equations

AU - Shimomura, Shun

PY - 2009

Y1 - 2009

N2 - We show that, under certain conditions, some difference Painlevé equations have nontrivial meromorphic solutions in the whole complex plane. These meromorphic solutions are obtained by analytic continuation of asymptotic solutions given in sectors of zero opening angle. The existence of these asymptotic solutions is shown by using fundamental matrix solutions of the associated linear systems with double unit characteristic roots and with coefficients expressed by asymptotic series in fractional powers.

AB - We show that, under certain conditions, some difference Painlevé equations have nontrivial meromorphic solutions in the whole complex plane. These meromorphic solutions are obtained by analytic continuation of asymptotic solutions given in sectors of zero opening angle. The existence of these asymptotic solutions is shown by using fundamental matrix solutions of the associated linear systems with double unit characteristic roots and with coefficients expressed by asymptotic series in fractional powers.

UR - http://www.scopus.com/inward/record.url?scp=70449558657&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449558657&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/42/31/315213

DO - 10.1088/1751-8113/42/31/315213

M3 - Article

AN - SCOPUS:70449558657

VL - 42

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 31

M1 - 315213

ER -