Y. Kodama, B. G. Konopelchenko, “Confluence of hypergeometric functions and integrable hydrodynamic-type systems”, TMF, 188:3 (2016), 429–455; Theoret. and Math. Phys., 188:3 (2016), 1334

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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 188, Number 3, Pages 429–455
DOI: https://doi.org/10.4213/tmf9076 (Mi tmf9076)

This article is cited in 15 scientific papers (total in 15 papers)

Confluence of hypergeometric functions and integrable hydrodynamic-type systems

Y. Kodama^a, B. G. Konopelchenko^b

^a Department of Mathematics, Ohio State University, Columbus, USA
^b Dipartimento di Matematica e Fisica "Ennio De Giorgi", Universita del Salento and INFN, Sezione di Lecce, Lecce, Italy

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DOI: https://doi.org/10.4213/tmf9076

Abstract: 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

G r (2, n)

$\mathrm{Gr}(2,n)$ , i. e., on the set of

2 \times n

$2\times n$ 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

G r (2, 5)

$\mathrm{Gr}(2,5)$ for two-component systems and

G r (2, 6)

$\mathrm{Gr}(2,6)$ for three-component systems in detail.

Keywords: Lauricella function, confluence, integrable system.

Funding agency	Grant number
National Science Foundation	DMS-1410267
PRIN	2010JJ4KBA_003
The research of Y. Kodama was supported in part by the National Science Foundation (NSF Grant No. DMS-1410267). The research of B. G. Konopelchenko was supported by PRIN 2010/2011 (Grant No. 2010JJ4KBA_003).

English version:
Theoretical and Mathematical Physics, 2016, Volume 188, Issue 3, Pages 1334–1357
DOI: https://doi.org/10.1134/S0040577916090051

Bibliographic databases:

PACS: 02.30.Ik

MSC: 14M15

Language: Russian

Citation: Y. Kodama, B. G. Konopelchenko, “Confluence of hypergeometric functions and integrable hydrodynamic-type systems”, TMF, 188:3 (2016), 429–455; Theoret. and Math. Phys., 188:3 (2016), 1334–1357

Citation in format AMSBIB

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This publication is cited in the following 15 articles:

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Paolo Lorenzoni, Sara Perletti, Karoline van Gemst, “Integrable Hierarchies and F-Manifolds with Compatible Connection”, Commun. Math. Phys., 406:4 (2025)
Paolo Lorenzoni, Sara Perletti, “Integrable hierarchies, Frölicher–Nijenhuis bicomplexes and Lauricella bi-flat F-manifolds”, Nonlinearity, 36:12 (2023), 6925
P. Vergallo, E. V. Ferapontov, “Hamiltonian systems of Jordan block type: Delta-functional reductions of the kinetic equation for soliton gas”, Journal of Mathematical Physics, 64:10 (2023)
Ferapontov V E., Pavlov V M., “Kinetic Equation For Soliton Gas: Integrable Reductions”, J. Nonlinear Sci., 32:2 (2022), 26
B.G. Konopelchenko, “Multi-dimensional Jordan chain and Navier-Stokes equation”, Physics Letters A, 441 (2022), 128167
B. G. Konopelchenko, G. Ortenzi, “On universality of homogeneous Euler equation”, J. Phys. A-Math. Theor., 54:20 (2021), 205701
M. V. Pavlov, P. Vergallo, R. Vitolo, “Classification of bi-Hamiltonian pairs extended by isometries”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 477:2251 (2021), 20210185
B. G. Konopelchenko, G. Ortenzi, “On the plane into plane mappings of hydrodynamic type. Parabolic case”, Rev. Math. Phys., 32:3 (2020), 2050006
L. Xue, E. V. Ferapontov, “Quasilinear systems of Jordan block type and the mKP hierarchy”, J. Phys. A-Math. Theor., 53:20 (2020), 205202
B. G. Konopelchenko, G. Ortenzi, “Parabolic regularization of the gradient catastrophes for the Burgers-Hopf equation and Jordan chain”, J. Phys. A-Math. Theor., 51:27 (2018), 275201, 26 pp.
M. V. Feigin, A. P. Veselov, “ $\vee$ -systems, holonomy Lie algebras, and logarithmic vector fields”, Int. Math. Res. Notices, 2018, no. 7, 2070–2098
Maxim V. Pavlov, “Integrability of exceptional hydrodynamic-type systems”, Proc. Steklov Inst. Math., 302 (2018), 325–335
M. V. Pavlov, N. M. Stoilov, “Three dimensional reductions of four-dimensional quasilinear systems”, J. Math. Phys., 58:11 (2017), 111510
B. G. Konopelchenko, G. Ortenzi, “Jordan form, parabolicity and other features of change of type transition for hydrodynamic type systems”, J. Phys. A-Math. Theor., 50:21 (2017), 215205

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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