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On two aspects of the Painleve analysis

Sergei Sakovich
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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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Sergei Sakovich. 2013-03-27. On two aspects of the Painleve analysis. https://doi.org/10.1155/2013%2F172813

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