RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2016, Volume 188, Number 3, Pages 429–455 (Mi tmf9076)  

This article is cited in 5 scientific papers (total in 5 papers)

Confluence of hypergeometric functions and integrable hydrodynamic-type systems

Y. Kodamaa, B. G. Konopelchenkob

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

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 $\mathrm{Gr}(2,n)$, 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, 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).

Author to whom correspondence should be addressed

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

Full text: PDF file (568 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2016, 188:3, 1334–1357

Bibliographic databases:

PACS: 02.30.Ik
MSC: 14M15

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
\Bibitem{KodKon16}
\by Y.~Kodama, B.~G.~Konopelchenko
\paper Confluence of hypergeometric functions and integrable hydrodynamic-type systems
\jour TMF
\yr 2016
\vol 188
\issue 3
\pages 429--455
\mathnet{http://mi.mathnet.ru/tmf9076}
\crossref{https://doi.org/10.4213/tmf9076}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3589011}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2016TMP...188.1334K}
\elib{http://elibrary.ru/item.asp?id=27350089}
\transl
\jour Theoret. and Math. Phys.
\yr 2016
\vol 188
\issue 3
\pages 1334--1357
\crossref{https://doi.org/10.1134/S0040577916090051}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000385628700005}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84989861977}


Linking options:
  • http://mi.mathnet.ru/eng/tmf9076
  • https://doi.org/10.4213/tmf9076
  • http://mi.mathnet.ru/eng/tmf/v188/i3/p429

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. M. V. Pavlov, N. M. Stoilov, “Three dimensional reductions of four-dimensional quasilinear systems”, J. Math. Phys., 58:11 (2017), 111510  crossref  mathscinet  zmath  isi  scopus
    2. 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  crossref  mathscinet  zmath  isi  scopus
    3. 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.  crossref  mathscinet  isi  scopus
    4. M. V. Feigin, A. P. Veselov, “$\vee$-systems, holonomy Lie algebras, and logarithmic vector fields”, Int. Math. Res. Notices, 2018, no. 7, 2070–2098  crossref  mathscinet  isi  scopus
    5. Maxim V. Pavlov, “Integrability of exceptional hydrodynamic-type systems”, Proc. Steklov Inst. Math., 302 (2018), 325–335  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:256
    Full text:11
    References:35
    First page:29

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019