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Tau-functions and generalized intergrable hierarchies

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Abstract

The tau-function formalism for a class of generalized “zero-curvature” integrable hierarchies of partial differential equations is constructed. The class includes the Drinfel'd-Sokolov hierarchies. A direct relation between the variables of the zero-curvature formalism and the tau-functions is established. The formalism also clarifies the connection between the zero-curvature hierarchies and the Hirotatype hierarchies of Kac and Wakimoto.

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Authors and Affiliations

  1. Theoretical Physics, 1 Keble Road, OX1 3NP, Oxford, U.K.

    Timothy Hollowood

  2. Theory Division, CERN, CH-1211, Geneva 23, Switzerland

    J. Luis Miramontes

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  1. Timothy Hollowood
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  2. J. Luis Miramontes
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Communicated by R.H. Dijkgraaf

Address after 1st October 1992: Theory Division, CERN, CH-1211 Geneva 23, Switzerland

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Hollowood, T., Miramontes, J.L. Tau-functions and generalized intergrable hierarchies. Commun.Math. Phys. 157, 99–117 (1993). https://doi.org/10.1007/BF02098021

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