International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1421-1434

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

Received 20 December 2004

Copyright © 2005 Huizeng Qin and Youmin Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.“