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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

New transformations for Painlevé's third transcendent


Author: N. S. Witte
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1649-1658
MSC (2000): Primary 34M55, 33E17; Secondary 20F55
Published electronically: January 27, 2004
MathSciNet review: 2051125
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Abstract: We present transformations relating the third transcendent of Painlevé with parameter sets located at the corners of the Weyl chamber for the symmetry group of the system, the affine Weyl group of the root system $B^{(1)}_2 $, to those at the origin. This transformation entails a scaling of the independent variable, and implies additive identities for the canonical Hamiltonians and product identities for the $\tau$-functions with these parameter sets.


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Additional Information

N. S. Witte
Affiliation: Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
Email: N.Witte@ms.unimelb.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07087-X
PII: S 0002-9939(04)07087-X
Keywords: Painlev\'e equations, B\"acklund transformations
Received by editor(s): January 26, 2002
Received by editor(s) in revised form: June 1, 2002
Published electronically: January 27, 2004
Communicated by: Mark J. Ablowitz
Article copyright: © Copyright 2004 American Mathematical Society