In this article, we study the solutions of difference Painleve equations I and II. to do this, we first give some properties of solutions to difference Riccati equations. We show that there are no rational solutions for the difference Painleve equation I. We also study rational solutions for the difference Painleve equation II. Later, we present a new way to seek solutions of the difference Painleve equation II by using the difference Riccati equation. At last, we construct new solutions of the difference Painleve equation II through a known solution.
Submitted April 28, 2016. Published September 28, 2016.
Math Subject Classifications: 39A10, 30D35, 39A12.
Key Words: Painleve difference equation; rational solution; Nevanlinna theory; difference Riccati equation; singularity confinement.
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| Zhi-Tao Wen |
Taiyuan University of Technology
Department of Mathematics
No. 79 Yingze West Street
030024 Taiyuan, China
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