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On some aspects of Bäcklund transformations
Authors:A. Mohammadi  E. Hesameddini
Affiliation:a Faculty of Mathematical Sciences, Tabriz University, Tabriz, Iran
b Faculty of Science, Shiraz University of Tech, Shiraz, Iran
Abstract:
The Painlevé differential equations (P2-P6) possess Bäcklund transformations which relate one solution to another solution either of the same equation, with different values of the parameters, or another such equation. We review a method for deriving difference equations, the discrete Painlevé equations in particular, from Bäcklund transformations of the continuous Painlevé equations. Then, we prove the existence of an algebraic formula relating three inconsecutive solutions of the same Bäcklund hierarchy for P3 and P4.
Keywords:Painlevé   differential equations    cklund transformation
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