The Painlevé test of nonlinear partial differential equations and its implementation using Maple

Abstract

The so-called WTC-Kruskal algorithm is presented in order to study the Painlevé integrability of nonlinear partial differential equations, which combines the WTC algorithm and Kruskal's simplification algorithm. Based on the WTC, Kruskal and WTC-Kruskal algorithms, we give an implementation in Maple called PDEPtest. The applications of PDEPtest to several nonlinear partial differential equations are also presented and some new results are reported. © Springer-Verlag Berlin Heidelberg 2005.