International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 18, Pages 69562, 10 p.
doi:10.1155/IJMMS/2006/69562
On the asymptotics of the real solutions to the general sixth Painlevé equation
Huizeng Qin1
and Youmin Lu2
1Department of Mathematics and Information Science, Shandong University of Technology, ZiBo, Shandong 255049, China
2Department of Mathematics and Computer Science, Bloomsburg University, Bloomsburg 17815, PA, USA
Abstract
We study the general sixth Painlevé equation, develop, and justify the existence of several groups of asymptotics of its real solutions. Our methods also justify the differentiability of the asymptotics. Particular attention is paid to the solutions between 0 and 1. We find the asymptotics of all real solutions between 0 and 1 of the sixth Painlevé equation as x→+∞.