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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
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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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http://mi.mathnet.ru/eng/tmf6416https://doi.org/10.4213/tmf6416 http://mi.mathnet.ru/eng/tmf/v161/i1/p21
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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A. V. Odesskii, V. V. Sokolov, “Integrable $(2+1)$-dimensional systems of hydrodynamic type”, Theoret. and Math. Phys., 163:2 (2010), 549–586
  -
Odesskii A.V., Sokolov V.V., “Classification of integrable hydrodynamic chains”, J. Phys. A, 43:43 (2010), 434027, 15 pp.
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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
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Akhmedova V. Takebe T. Zabrodin A., “Multi-Variable Reductions of the Dispersionless DKP Hierarchy”, J. Phys. A-Math. Theor., 50:48 (2017), 485204
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