Journal of Nonlinear Mathematical Physics

Volume 13, Issue 1, February 2006, Pages 90 - 110

Symbolic Software for the Painlevé Test of Nonlinear Ordinary and Partial Differential Equations

Authors
Douglas BALDWIN, Willy HEREMAN
Corresponding Author
Douglas BALDWIN
Available Online 28 November 2006.
DOI
https://doi.org/10.2991/jnmp.2006.13.1.8How to use a DOI?
Abstract
The automation of the traditional Painlev´e 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 Painlev´e test, and these omissions often lead to erroneous results. Finally, our package is compared with the other available implementations of the Painlev´e test.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
13 - 1
Pages
90 - 110
Publication Date
2006/11
ISSN
1402-9251
DOI
https://doi.org/10.2991/jnmp.2006.13.1.8How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Douglas BALDWIN
AU  - Willy HEREMAN
PY  - 2006
DA  - 2006/11
TI  - Symbolic Software for the Painlevé Test of Nonlinear Ordinary and Partial Differential Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 90
EP  - 110
VL  - 13
IS  - 1
SN  - 1402-9251
UR  - https://doi.org/10.2991/jnmp.2006.13.1.8
DO  - https://doi.org/10.2991/jnmp.2006.13.1.8
ID  - BALDWIN2006
ER  -