On Two Aspects of the Painlevé Analysis | Zendy

Sergei Sakovich | Zendy

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On Two Aspects of the Painlevé Analysis

Author(s) -

Sergei Sakovich

Publication year - 2013

Publication title -

international journal of analysis

Language(s) - English

Resource type - Journals

eISSN - 2314-4998

pISSN - 2314-498X

DOI - 10.1155/2013/172813

Subject(s) - mathematics , truncation (statistics) , transformation (genetics) , nonlinear system , pure mathematics , lax pair , mathematical analysis , algebra over a field , integrable system , statistics , chemistry , biochemistry , physics , quantum mechanics , gene

We use the Calogero equation to illustrate the following two aspects of thePainleve analysis of nonlinear PDEs. First, if a nonlinear equation passes thePainleve test for integrability, the singular expansions of its solutionsaround characteristic hypersurfaces can be neither single-valued functions ofindependent variables nor single-valued functionals of data. Second, if thetruncation of singular expansions of solutions is consistent, the truncationnot necessarily leads to the simplest, or elementary, auto-Backlundtransformation related to the Lax pair.Comment: 8 page

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