International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 13, Pages 845-851
doi:10.1155/S0161171203206220

On the asymptotic representation of the solutions to the fourth general Painlevé equation

Youmin Lu

 Department of Mathematics, Computer Science and Statistics, College of Science and Technology, Bloomsburg University of Pennsylvania, Bloomsburg 17815, PA, USA
Received 5 June 2002

Abstract

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.