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TMF, 2008, Volume 154, Number 2, Pages 249–260 (Mi tmf6166)  

This article is cited in 10 scientific papers (total in 10 papers)

Classification of integrable Vlasov-type equations

A. V. Odesskiiab, M. V. Pavlovc, V. V. Sokolova

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b University of Manchester
c P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: The classification of integrable Vlasov-type equations reduces to a functional equation for a generating function. We find a general solution of this functional equation in terms of hypergeometric functions.

Keywords: integrable hydrodynamic chain, hydrodynamic reduction

DOI: https://doi.org/10.4213/tmf6166

Full text: PDF file (420 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2008, 154:2, 209–219

Bibliographic databases:

Received: 24.04.2007
Revised: 28.10.2007

Citation: A. V. Odesskii, M. V. Pavlov, V. V. Sokolov, “Classification of integrable Vlasov-type equations”, TMF, 154:2 (2008), 249–260; Theoret. and Math. Phys., 154:2 (2008), 209–219

Citation in format AMSBIB
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    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. Maxim V. Pavlov, Ziemowit Popowicz, “On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems”, SIGMA, 5 (2009), 011, 10 pp.  mathnet  crossref  mathscinet  zmath
    2. A. V. Odesskii, V. V. Sokolov, “Integrable elliptic pseudopotentials”, Theoret. and Math. Phys., 161:1 (2009), 1340–1352  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Odesskii A.V., Sokolov V.V., “Integrable pseudopotentials related to generalized hypergeometric functions”, Selecta Math. (N.S.), 16:1 (2010), 145–172  crossref  mathscinet  zmath  isi  scopus
    4. A. V. Odesskii, V. V. Sokolov, “Integrable $(2+1)$-dimensional systems of hydrodynamic type”, Theoret. and Math. Phys., 163:2 (2010), 549–586  mathnet  crossref  crossref  adsnasa  isi  elib
    5. El G.A., Kamchatnov A.M., Pavlov M.V., Zykov S.A., “Kinetic equation for a soliton gas and its hydrodynamic reductions”, J. Nonlinear Sci., 21:2 (2011), 151–191  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. 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  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. V. V. Vedenyapin, M. A. Negmatov, N. N. Fimin, “Vlasov-type and Liouville-type equations, their microscopic, energetic and hydrodynamical consequences”, Izv. Math., 81:3 (2017), 505–541  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. Bulchandani V.B., “On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems”, J. Phys. A-Math. Theor., 50:43 (2017), 435203  crossref  mathscinet  zmath  isi  scopus
    9. N. N. Fimin, V. M. Chechetkin, “Cistemy kvazilineinykh uravnenii s odinakovoi glavnoi chastyu i gidrodinamicheskaya podstanovka”, Preprinty IPM im. M. V. Keldysha, 2018, 055, 12 pp.  mathnet  crossref
    10. N. N. Fimin, V. M. Chechetkin, “Primenenie gidrodinamicheskoi podstanovki dlya sistem uravnenii s odinakovoi glavnoi chastyu”, Nelineinaya dinam., 14:1 (2018), 53–61  mathnet  crossref  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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