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Funktsional'nyi Analiz i ego Prilozheniya, 1991, Volume 25, Issue 3, Pages 37–49 (Mi faa879)  

This article is cited in 74 scientific papers (total in 74 papers)

Differential geometry of nonlocal Hamiltonian operators of hydrodynamic type

E. V. Ferapontov

Computing Centre, USSR Academy of Sciences
References:
Received: 29.08.1990
English version:
Functional Analysis and Its Applications, 1991, Volume 25, Issue 3, Pages 195–204
DOI: https://doi.org/10.1007/BF01085489
Bibliographic databases:
Document Type: Article
UDC: 514.8
Language: Russian
Citation: E. V. Ferapontov, “Differential geometry of nonlocal Hamiltonian operators of hydrodynamic type”, Funktsional. Anal. i Prilozhen., 25:3 (1991), 37–49; Funct. Anal. Appl., 25:3 (1991), 195–204
Citation in format AMSBIB
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\by E.~V.~Ferapontov
\paper Differential geometry of nonlocal Hamiltonian operators of hydrodynamic type
\jour Funktsional. Anal. i Prilozhen.
\yr 1991
\vol 25
\issue 3
\pages 37--49
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1139873}
\zmath{https://zbmath.org/?q=an:0742.58018}
\transl
\jour Funct. Anal. Appl.
\yr 1991
\vol 25
\issue 3
\pages 195--204
\crossref{https://doi.org/10.1007/BF01085489}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1991GX74100005}
Linking options:
  • https://www.mathnet.ru/eng/faa879
  • https://www.mathnet.ru/eng/faa/v25/i3/p37
  • This publication is cited in the following 74 articles:
    1. Thibault Bonnemain, Vincent Caudrelier, Benjamin Doyon, “Hamiltonian Formulation and Aspects of Integrability of Generalised Hydrodynamics”, Ann. Henri Poincaré, 2025  crossref
    2. Kostyantyn M. Kulyk, Vladimir V. Yanovsky, “Two-Dimensional Hydrodynamics as a Class of Special Hamiltonian Systems”, East Eur. J. Phys., 2024, no. 2, 134  crossref
    3. E. V. Glukhov, O. I. Mokhov, “Algebraic-geometry approach to construction of semi-Hamiltonian systems of hydrodynamic type”, Izv. Math., 87:6 (2023), 1148–1160  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. E. V. Glukhov, “On an Algebro-Geometric Approach to Ribaucour Transformations and Bianchi Cubes”, Math. Notes, 111:5 (2022), 722–728  mathnet  crossref  crossref  mathscinet
    5. A. M. Gagonov, O. I. Mokhov, “On compatible diagonal metrics”, Russian Math. Surveys, 76:6 (2021), 1140–1142  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. Arsie A. Buryak A. Lorenzoni P. Rossi P., “Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics”, Int. Math. Res. Notices, 2021  crossref  isi
    7. Maltsev A.Ya. Novikov S.P., “Poisson Brackets of Hydrodynamic Type and Their Generalizations”, J. Exp. Theor. Phys., 132:4, SI (2021), 645–657  crossref  isi
    8. Si-Qi Liu, Zhe Wang, Youjin Zhang, “Super tau-covers of bihamiltonian integrable hierarchies”, Journal of Geometry and Physics, 170 (2021), 104351  crossref
    9. E. V. Glukhov, O. I. Mokhov, “On algebraic-geometry methods for constructing submanifolds with flat normal bundle and holonomic net of curvature lines”, Funct. Anal. Appl., 54:3 (2020), 169–178  mathnet  crossref  crossref  mathscinet  isi
    10. Casati M., Lorenzoni P., Vitolo R., “Three Computational Approaches to Weakly Nonlocal Poisson Brackets”, Stud. Appl. Math., 144:4 (2020), 412–448  crossref  isi
    11. Riccardo Ontani, “Some remarks on the operator formalism for nonlocal Poisson brackets”, Journal of Mathematical Physics, 61:9 (2020)  crossref
    12. P. Lorenzoni, R. Vitolo, “Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds”, Journal of Geometry and Physics, 149 (2020), 103573  crossref
    13. E. V. Glukhov, O. I. Mokhov, “On algebraic-geometry methods for constructing flat diagonal metrics of a special form”, Russian Math. Surveys, 74:4 (2019), 761–763  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. Arsie A., Lorenzoni P., “F-Manifolds, Multi-Flat Structures and Painleve Transcendents”, Asian J. Math., 23:5 (2019), 877–904  isi
    15. Maxim V Pavlov, Raffaele F Vitolo, “Bi-Hamiltonian structure of the oriented associativity equation”, J. Phys. A: Math. Theor., 52:20 (2019), 20LT01  crossref
    16. O. I. Mokhov, “Pencils of compatible metrics and integrable systems”, Russian Math. Surveys, 72:5 (2017), 889–937  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. Bulchandani V.B., “On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems”, J. Phys. A-Math. Theor., 50:43 (2017), 435203  crossref  isi
    18. M.B. Sheftel, D. Yaz{\i}cı, A.A. Malykh, “Recursion operators and bi-Hamiltonian structure of the general heavenly equation”, Journal of Geometry and Physics, 116 (2017), 124  crossref
    19. Mikhail B. Sheftel, Devrim Yazici, “Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański”, SIGMA, 12 (2016), 091, 17 pp.  mathnet  crossref
    20. I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175  mathnet  crossref  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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