Meromorphic solutions of difference Painlevé equations

Shun Shimomura

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 languageEnglish
Article number315213
JournalJournal of Physics A: Mathematical and Theoretical
Issue number31
Publication statusPublished - 2009 Nov 20

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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