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International Journal of Analysis
Volume 2013, Article ID 172813, 5 pages
http://dx.doi.org/10.1155/2013/172813
Research Article

On Two Aspects of the Painlevé Analysis

Institute of Physics, National Academy of Sciences of Belarus, 220072 Minsk, Belarus

Received 13 September 2012; Accepted 6 February 2013

Academic Editor: Baruch Cahlon

Copyright © 2013 Sergei Sakovich. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We use the Calogero equation to illustrate the following two aspects of the Painlevé analysis of nonlinear PDEs. First, if a nonlinear equation passes the Painlevé test for integrability, the singular expansions of its solutions around characteristic hypersurfaces can be neither single-valued functions of independent variables nor single-valued functionals of data. Second, if the truncation of singular expansions of solutions is consistent, the truncation not necessarily leads to the simplest, or elementary, auto-Bäcklund transformation related to the Lax pair.