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TMF, 2009, Volume 161, Number 1, Pages 21–36 (Mi tmf6416)  

This article is cited in 4 scientific papers (total in 4 papers)

Integrable elliptic pseudopotentials

A. V. Odesskiiab, V. V. Sokolova

a 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

DOI: https://doi.org/10.4213/tmf6416

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

Bibliographic databases:

Received: 11.11.2008

Citation: A. V. Odesskii, V. V. Sokolov, “Integrable elliptic pseudopotentials”, TMF, 161:1 (2009), 21–36; Theoret. and Math. Phys., 161:1 (2009), 1340–1352

Citation in format AMSBIB
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\paper Integrable elliptic pseudopotentials
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\transl
\jour Theoret. and Math. Phys.
\yr 2009
\vol 161
\issue 1
\pages 1340--1352
\crossref{https://doi.org/10.1007/s11232-009-0120-5}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Odesskii, V. V. Sokolov, “Integrable $(2+1)$-dimensional systems of hydrodynamic type”, Theoret. and Math. Phys., 163:2 (2010), 549–586  mathnet  crossref  crossref  adsnasa  isi  elib
    2. Odesskii A.V., Sokolov V.V., “Classification of integrable hydrodynamic chains”, J. Phys. A, 43:43 (2010), 434027, 15 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Ferapontov E.V., Odesskii A.V., Stoilov N.M., “Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions”, J Math Phys, 52:7 (2011), 073505  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Akhmedova V. Takebe T. Zabrodin A., “Multi-Variable Reductions of the Dispersionless DKP Hierarchy”, J. Phys. A-Math. Theor., 50:48 (2017), 485204  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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