On Two Aspects of the Painlevé Analysis

Sergei Sakovich

International Journal of Analysis, 2013, vol. 2013, 1-5

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:ijanal:172813

DOI: 10.1155/2013/172813

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