Sunday, April 15, 2012

9909027 (Sergei Sakovich)

On two aspects of the Painleve analysis    [PDF]

Sergei Sakovich
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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