Geodesic
Integrable elliptic pseudopotentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 1, pp. 21-36

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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. 
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     author = {A. V. Odesskii and V. V. Sokolov},
     title = {Integrable elliptic pseudopotentials},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2009_161_1_a1/}
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A. V. Odesskii; V. V. Sokolov. Integrable elliptic pseudopotentials. Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 1, pp. 21-36. http://geodesic.mathdoc.fr/item/TMF_2009_161_1_a1/