International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 13, Pages 845-851
On the asymptotic representation of the solutions to the fourth
general Painlevé equation
Department of Mathematics, Computer Science and Statistics, College of Science and Technology, Bloomsburg University of Pennsylvania, Bloomsburg 17815, PA, USA
Received 5 June 2002
Copyright © 2003 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.
There have been many results on the asymptotics of the
Painlevé transcendents in recent years, but the asymptotics
of the fourth Painlevé transcendent has not been studied
much. In this note, we study the general fourth Painlevé
equation and develop an asymptotic representation of a group of
its solutions as the independent variable approaches infinity
along a straight line.