Journal of Nonlinear Mathematical Physics

Volume 9, Issue Supplement 2, September 2001, Pages 36 - 48

Singularity Analysis and a Function Unifying

Authors
the Painlevé, the Psi Series
Corresponding Author
the Painlevé
Available Online 1 September 2001.
DOI
https://doi.org/10.2991/jnmp.2002.9.s2.4How to use a DOI?
Abstract
The classical (ARS) algorithm used in the Painlevé test picks up only those functions analytic in the complex plane. We complement it with an iterative algorithm giving the leading order and the next terms in all cases. This algorithm works both for an ascending series (about a singularity at finite time) and a descending series (asymptotic expansion for t ). The algorithm introduces naturally the logarithmic terms when they are necessary. The calculation, given in the first place for a system possessing the two symmetries of time translation and self-similarity, is subsequently generalised to the case in which this last symmetry is broken. The algorithm enlarges the class of equations for which more explicit methods (Lie symmetries, Darboux and Carleman invariants etc) should be applied with a certain hope of success.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - 100
Pages
36 - 48
Publication Date
2001/09
ISBN
91-631-2869-1
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2002.9.s2.4How 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  - the Painlevé
AU  - the Psi Series
PY  - 2001
DA  - 2001/09
TI  - Singularity Analysis and a Function Unifying
JO  - Journal of Nonlinear Mathematical Physics
SP  - 36
EP  - 48
VL  - 9
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.s2.4
DO  - https://doi.org/10.2991/jnmp.2002.9.s2.4
ID  - Painlevé2001
ER  -