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Integrable elliptic pseudopotentials

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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.

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia

    A. V. Odesskii & V. V. Sokolov

  2. Brock University, St. Catharines, Ontario, Canada

    A. V. Odesskii

Authors
  1. A. V. Odesskii
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  2. V. V. Sokolov
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Correspondence to A. V. Odesskii.

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__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 161, No. 1, pp. 21–36, October, 2009.

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Odesskii, A.V., Sokolov, V.V. Integrable elliptic pseudopotentials. Theor Math Phys 161, 1340–1352 (2009). https://doi.org/10.1007/s11232-009-0120-5

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  • DOI: https://doi.org/10.1007/s11232-009-0120-5

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