On two aspects of the Painleve analysis
solv-int
2013-03-28 v3 Mathematical Physics
Analysis of PDEs
math.MP
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.solv-int/9909027,
title = {On two aspects of the Painleve analysis},
author = {Sergei Sakovich},
journal= {arXiv preprint arXiv:solv-int/9909027},
year = {2013}
}
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8 pages