Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 5 (2009), 024, 11 pages      arXiv:0903.0342      http://dx.doi.org/10.3842/SIGMA.2009.024

Bäcklund Transformations for First and Second Painlevé Hierarchies

Ayman Hashem Sakka
Department of Mathematics, Islamic University of Gaza, P.O. Box 108, Rimal, Gaza, Palestine

Received November 25, 2008, in final form February 24, 2009; Published online March 02, 2009

Abstract
We give Bäcklund transformations for first and second Painlevé hierarchies. These Bäcklund transformations are generalization of known Bäcklund transformations of the first and second Painlevé equations and they relate the considered hierarchies to new hierarchies of Painlevé-type equations.

Key words: Painlevé hierarchies; Bäcklund transformations.

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