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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, M. Tabor and 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.

35Q99 Partial differential equations of mathematical physics and other areas of application
Full Text: DOI
[1] DOI: 10.1063/1.525721 · Zbl 0514.35083 · doi:10.1063/1.525721
[2] DOI: 10.1063/1.525389 · Zbl 0492.70019 · doi:10.1063/1.525389
[3] DOI: 10.1002/cpa.3160320202 · Zbl 0388.34005 · doi:10.1002/cpa.3160320202
[4] DOI: 10.1063/1.522808 · Zbl 0347.76011 · doi:10.1063/1.522808
[5] DOI: 10.1063/1.523297 · Zbl 0361.35017 · doi:10.1063/1.523297
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[7] Dryuma V. S., JETP Lett. 19 pp 387– (1974)
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