Finite-order meromorphic solutions and the discrete Painleve equations |
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Authors: | Halburd R G; Korhonen R J |
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Institution: | 1 Department of Mathematical Sciences Loughborough University Loughborough Leicestershire LE11 3TU United Kingdom R.G.Halburd{at}lboro.ac.uk
2 Department of Mathematics University of Joensuu P.O. Box 111 FI-80101 Joensuu Finland risto.korhonen{at}joensuu.fi |
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Abstract: | Let w(z) be an admissible finite-order meromorphic solutionof the second-order difference equation
![Formula 012UM1](http://plms.oxfordjournals.org/content/vol94/issue2/images/medium/pdl01201.gif) where R(z, w(z)) is rational in w(z) withcoefficients that are meromorphic in z. Then either w(z) satisfiesa difference linear or Riccati equation or else the above equationcan be transformed to one of a list of canonical differenceequations. This list consists of all known difference Painlevéequations of the above form, together with their autonomousversions. This suggests that the existence of finite-order meromorphicsolutions is a good detector of integrable difference equations. |
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