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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.

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
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[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
[6] Dryuma V. S., Pis’ma Zh. Eksp. Teor. Fiz. 19 pp 753– (1974)
[7] Dryuma V. S., JETP Lett. 19 pp 387– (1974)
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