A constructive REDUCE package based upon the Painlevé analysis of nonlinear evolutions equations in Hamiltonian and / or normal form

A number of necessary conditions for scalar nonlinear evolution equations of normal or certain Hamiltonian form to pass the Painlevé test in one (or two) branches with the Kruskal ansatz is used to write a REDUCE package able to construct (theoretically) all equations with this property. Starting wi...

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Bibliographic Details
Published in:Computer physics communications 1992-06, Vol.70 (2), p.409-416
Main Author: Renner, Friedrich
Format: Article
Language:English
Subjects:
Computational techniques
Exact sciences and technology
Mathematical methods in physics
Physics
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Summary:A number of necessary conditions for scalar nonlinear evolution equations of normal or certain Hamiltonian form to pass the Painlevé test in one (or two) branches with the Kruskal ansatz is used to write a REDUCE package able to construct (theoretically) all equations with this property. Starting with a given leading order, a degree of homogeneity and (in the Hamiltonian case) a skew-adjoint differential operator, the system generates all admissible resonance patterns, adapts (if possible) the free parameters of the equation according to the chosen pattern and the constraints of the compatibility conditions. In the Painlevé case, the general inhomogeneous equation is generated and also examined. For help and further investigations a set of utility procedures is supplied.
ISSN:0010-4655
1879-2944
DOI:10.1016/0010-4655(92)90203-B