Meromorphic solutions of difference Painlevé equations

Shun Shimomura

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Article number315213
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number31
DOIs
Publication statusPublished - 2009

Fingerprint

Meromorphic Solution
difference equations
Asymptotics of Solutions
Difference equations
Difference equation
Zero angle
Characteristic Roots
Fundamental Matrix
Asymptotic series
Fractional Powers
Unit Root
Analytic Continuation
Argand diagram
asymptotic series
Sector
Linear Systems
linear systems
Linear systems
sectors
Coefficient

ASJC Scopus subject areas

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

Cite this

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

In: Journal of Physics A: Mathematical and Theoretical, Vol. 42, No. 31, 315213, 2009.

Research output: Contribution to journalArticle

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