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Zbl 0531.35069
Weiss, John
The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative. (English)
[J] J. Math. Phys. 24, 1405-1413 (1983). ISSN 0022-2488; ISSN 1089-7658/e

[For part I see the author, {\it M. Tabor} and {\it G. Carnevale}, ibid. 522-526 (1983; Zbl 0514.35083).] \par In this paper we investigate the Painlevé property for partial differential equations. By application to several well-known (integrable) partial differential equations it is shown that a Bäcklund transform defined by expansions about the "singular manifold" leads to a formulation of these equations in terms of the "Schwarzian derivative". This formulation is invariant under the Möbius group and obtains the appropriate Lax pair (linearization) for the underlying pde.

MSC 2000:: *35Q99 PDE of mathematical physics and other areas

Keywords: Painlevé property; Bäcklund transformation; Lax pairs; Schwarzian derivative; integrable partial differential equations; Möbius group

Citations: Zbl 0514.35083

Cited in: Zbl 1239.35165 Zbl 0738.58052 Zbl 0727.35132

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