This article is cited in 5 papers

Integrable elliptic pseudopotentials

A. V. Odesskii^ab, V. V. Sokolov<sup>a

a</sup> L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, Russia
^b Brock University, St. Catharines, Ontario, Canada

Abstract: We construct integrable pseudopotentials with an arbitrary number of fields in terms of an elliptic generalization of hypergeometric functions in several variables. These pseudopotentials are multiparameter deformations of ones constructed by Krichever in studying the Whitham-averaged solutions of the KP equation and yield new integrable $(2{+}1)$-dimensional systems of hydrodynamic type. Moreover, an interesting class of integrable $(1{+}1)$-dimensional systems described in terms of solutions of an elliptic generalization of the Gibbons–Tsarev system is related to these pseudopotentials.

Keywords: integrable three-dimensional system of hydrodynamic type, elliptic hypergeometric function.

Received: 11.11.2008

DOI: 10.4213/tmf6416

 English version: Theoretical and Mathematical Physics, 2009, 161:1, 1340–1352

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