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VOL. 61 | 2011 Differential Fay identities and auxiliary linear problem of integrable hierarchies
Kanehisa Takasaki

Editor(s) Koji Hasegawa, Takahiro Hayashi, Shinobu Hosono, Yasuhiko Yamada


We review the notion of differential Fay identities and demonstrate, through case studies, its new role in integrable hierarchies of the KP type. These identities are known to be a convenient tool for deriving dispersionless Hirota equations. We show that differential (or, in the case of the Toda hierarchy, difference) Fay identities play a more fundamental role. Namely, they are nothing but a generating functional expression of the full set of auxiliary linear equations, hence substantially equivalent to the integrable hierarchies themselves. These results are illustrated for the KP, Toda, BKP and DKP hierarchies. As a byproduct, we point out some new features of the DKP hierarchy and its dispersionless limit.


Published: 1 January 2011
First available in Project Euclid: 24 November 2018

zbMATH: 1259.37043
MathSciNet: MR2867153

Digital Object Identifier: 10.2969/aspm/06110387

Rights: Copyright © 2011 Mathematical Society of Japan


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