International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1421-1434
doi:10.1155/IJMMS.2005.1421
Application of uniform asymptotics method to analyzing the asymptotic behaviour of the general fourth Painlevé transcendent
Huizeng Qin1
and Youmin Lu2
1Department of Mathematical and Information Science, Shandong University of Technology, Shandong, Zibo, China
2Department of Mathematics and Statistics, Bloomsburg University, Bloomsburg 17815, PA, USA
Abstract
We use the uniform asymptotics method proposed by A. P. Bassom et al. (1998) to study the general fourth Painlevé transcendent, find a group of its asymptotics and the corresponding monodromic data, and prove its existence and ”uniqueness.“