Geodesic
Confluence of hypergeometric functions and integrable hydrodynamic-type systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 3, pp. 429-455

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We construct a new class of integrable hydrodynamic-type systems governing the dynamics of the critical points of confluent Lauricella-type functions defined on finite-dimensional Grassmannian $\mathrm{Gr}(2,n)$, i. e., on the set of $2\times n$ matrices of rank two. These confluent functions satisfy certain degenerate Euler–Poisson–Darboux equations. We show that in the general case, a hydrodynamic-type system associated with the confluent Lauricella function is an integrable and nondiagonalizable quasilinear system of a Jordan matrix form. We consider the cases of the Grassmannians $\mathrm{Gr}(2,5)$ for two-component systems and $\mathrm{Gr}(2,6)$ for three-component systems in detail.
Keywords: Lauricella function, integrable system.
Mots-clés : confluence 
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     author = {Y. Kodama and B. G. Konopelchenko},
     title = {Confluence of hypergeometric functions and integrable hydrodynamic-type systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {429--455},
     publisher = {mathdoc},
     volume = {188},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a4/}
}
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Y. Kodama; B. G. Konopelchenko. Confluence of hypergeometric functions and integrable hydrodynamic-type systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 3, pp. 429-455. http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a4/