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Symbolic Software for the Painleve Test of Nonlinear Ordinary and Partial Differential Equations
The automation of the traditional Painleve test in Mathematica is discussed.
The package PainleveTest.m allows for the testing of polynomial systems of
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.Comment: Published in the Journal of Nonlinear Mathematical Physics
(http://www.sm.luth.se/math/JNMP/), vol. 13(1), pp. 90-110 (Feb. 2006). The
software can be downloaded at either http://www.douglasbaldwin.com or
http://www.mines.edu/fs_home/wherema
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