Singularity Analysis and a Function Unifying

DOI

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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - C. Géronimi
AU  - P.G.L. Leach
AU  - M.R. Feix
PY  - 2002
DA  - 2002/09/02
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  - 10.2991/jnmp.2002.9.s2.4
ID  - Géronimi2002
ER  -