Existence of zero-order meromorphic solutions in detecting $q$-difference Painlevé equations
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- by Risto Korhonen and Zhi-Tao Wen PDF
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Abstract:
The existence of zero-order meromorphic solutions is used as a sufficient condition in detecting $q$-difference equations of Painlevé type. It is shown that demanding the existence of at least one non-rational zero-order meromorphic solution $w(z)$ is sufficient to reduce a canonical class of $q$-difference equations with rational coefficients into a short list of Painlevé type $q$-difference equations, unless $w(z)$ is simultaneously a solution of a $q$-difference Riccati equation of a specific form.References
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Additional Information
- Risto Korhonen
- Affiliation: Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
- MR Author ID: 702144
- Email: risto.korhonen@uef.fi
- Zhi-Tao Wen
- Affiliation: Department of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, People’s Republic of China
- MR Author ID: 917720
- Email: zhitaowen@gmail.com
- Received by editor(s): September 13, 2013
- Received by editor(s) in revised form: June 3, 2014
- Published electronically: October 28, 2015
- Additional Notes: The first author was supported in part by the Academy of Finland grant number 268009, and the second author was supported in part by China Scholarship Council (CSC)
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 4993-5008
- MSC (2010): Primary 39A13; Secondary 33E17, 30D35
- DOI: https://doi.org/10.1090/tran/6491
- MathSciNet review: 3456168