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On two aspects of the Painleve analysis

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Type
Published Article
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Identifiers
DOI: 10.1155/2013/172813
arXiv ID: solv-int/9909027
Source
arXiv
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Abstract

We use the Calogero equation to illustrate the following two aspects of the Painleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the Painleve 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-Backlund transformation related to the Lax pair.

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