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The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative. (English) Zbl 0531.35069
[For part I see the author, {\it M. Tabor} and {\it G. Carnevale}, ibid. 522-526 (1983; Zbl 0514.35083).] 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:
 35Q99 PDE of mathematical physics and other areas
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