On two aspects of the Painleve analysis

Details On two aspects of the Painleve analysis On two aspects of the Painleve analysis

1999-09-26

arxiv.org/abs/solv-int/9909027v2

Physics

Mathematical Physics

8 pages

Scientific paper

We use the Calogero equation to illustrate the following two aspects of the Painleve analysis of nonlinear PDEs. First, even if a nonlinear equation is integrable, the singular expansions of its solutions around characteristic hypersurfaces are neither single-valued functions of independent variables nor single-valued functionals of data. Second, even 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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