Symbolic Software for the Painlevé Test of Nonlinear Ordinary and Partial Differential Equations
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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.
- © 2006, the Authors. Published by Atlantis Press.
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- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Douglas Baldwin AU - Willy Hereman PY - 2006 DA - 2006/02/01 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 - 1776-0852 UR - https://doi.org/10.2991/jnmp.2006.13.1.8 DO - 10.2991/jnmp.2006.13.1.8 ID - Baldwin2006 ER -