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Title

Symbolic software for the Painleve test of nonlinear ordinary and partial differential equations
Authors

D. Baldwin
Willy Hereman
Organization: Colorado School of Mines
Department: Department of Mathematical and Computer Sciences
Journal / Anthology

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
Year: 2006
Volume: 13
Issue: 1
Page range: 90-110
Description

The automation of the traditional Painleve test in Mathematica is discussed. The package PainleveTest.m allows for the testing of polynomial systems of nonlinear ordinary and partial differential equations which may be parameterized by arbitrary functions ( or constants). Except where limited by memory, there is no restriction on the number of independent or dependent variables. The package is quite robust in determining all the possible dominant behaviors of the Laurent series solutions of the differential equation. The omission of valid dominant behaviors is a common problem in many implementations of the Painleve test, and these omissions often lead to erroneous results. Finally, our package is compared with the other available implementations of the Painleve test.
Subjects

*Mathematica Technology > Programming > Packages and Contexts
*Mathematics > Calculus and Analysis > Differential Equations
Keywords

Painlevé test, Korteweg-deVries equation, Hirota-Satsuma system