On two aspects of the Painleve analysis
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 singlevalued functions of independent variables nor singlevalued functionals of data. Second, if the truncation of singular expansions of solutions is consistent, the truncation not necessarily leads to the simplest, or elementary, autoBacklund transformation related to the Lax pair.
 Publication:

arXiv eprints
 Pub Date:
 September 1999
 arXiv:
 arXiv:solvint/9909027
 Bibcode:
 1999solv.int..9027S
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics;
 Mathematics  Analysis of PDEs
 EPrint:
 8 pages