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Tr. Mat. Inst. Steklova, 1999, Volume 225, Pages 284–300 (Mi tm727)  

This article is cited in 24 scientific papers (total in 24 papers)

Compatible Poisson Structures of Hydrodynamic Type and Associativity Equations

O. I. Mokhov

Landau Institute for Theoretical Physics, Centre for Non-linear Studies

Full text: PDF file (2307 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 1999, 225, 269–284

Bibliographic databases:
UDC: 517.9+514.7
Received in December 1998

Citation: O. I. Mokhov, “Compatible Poisson Structures of Hydrodynamic Type and Associativity Equations”, Solitons, geometry, and topology: on the crossroads, Collection of papers dedicated to the 60th anniversary of academician Sergei Petrovich Novikov, Tr. Mat. Inst. Steklova, 225, Nauka, MAIK Nauka/Inteperiodika, M., 1999, 284–300; Proc. Steklov Inst. Math., 225 (1999), 269–284

Citation in format AMSBIB
\Bibitem{Mok99}
\by O.~I.~Mokhov
\paper Compatible Poisson Structures of Hydrodynamic Type and Associativity Equations
\inbook Solitons, geometry, and topology: on the crossroads
\bookinfo Collection of papers dedicated to the 60th anniversary of academician Sergei Petrovich Novikov
\serial Tr. Mat. Inst. Steklova
\yr 1999
\vol 225
\pages 284--300
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm727}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1725947}
\zmath{https://zbmath.org/?q=an:0985.37071}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1999
\vol 225
\pages 269--284


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. I. Mokhov, “Compatible and almost compatible metrics”, Russian Math. Surveys, 55:4 (2000), 819–821  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. O. I. Mokhov, “Compatible and Almost Compatible Pseudo-Riemannian Metrics”, Funct. Anal. Appl., 35:2 (2001), 100–110  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. O. I. Mokhov, “Flat pencils of metrics and integrable reductions of Lamé's equations”, Russian Math. Surveys, 56:2 (2001), 416–418  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. O. I. Mokhov, “Compatible Dubrovin–Novikov Hamiltonian operators and the Lie derivative”, Russian Math. Surveys, 56:6 (2001), 1175–1176  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Fordy A.P., Mokhov O.I., “On a special class of compatible Poisson structures of hydrodynamic type”, Physica D–Nonlinear Phenomena, 152 (2001), 475–490  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Ferapontov E.V., “Compatible Poisson brackets of hydrodynamic type”, Journal of Physics A–Mathematical and General, 34:11 (2001), 2377–2388  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. O. I. Mokhov, “Integrability of the Equations for Nonsingular Pairs of Compatible Flat Metrics”, Theoret. and Math. Phys., 130:2 (2002), 198–212  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. O. I. Mokhov, “Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Hierarchies Related to Them”, Theoret. and Math. Phys., 132:1 (2002), 942–954  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. O. I. Mokhov, “Compatible Dubrovin–Novikov Hamiltonian Operators, Lie Derivative, and Integrable Systems of Hydrodynamic Type”, Theoret. and Math. Phys., 133:2 (2002), 1557–1564  mathnet  crossref  crossref  mathscinet  isi  elib
    10. O. I. Mokhov, “Integrable bi-Hamiltonian systems of hydrodynamic type”, Russian Math. Surveys, 57:1 (2002), 153–154  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. O. I. Mokhov, “Integrable bi-Hamiltonian hierarchies generated by compatible metrics of constant Riemannian curvature”, Russian Math. Surveys, 57:5 (2002), 999–1001  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    12. O. I. Mokhov, “Quasi-Frobenius Algebras and Their Integrable $N$-Parameter Deformations Generated by Compatible $(N\times N)$ Metrics of Constant Riemannian Curvature”, Theoret. and Math. Phys., 136:1 (2003), 908–916  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. O. I. Mokhov, “The Liouville Canonical Form for Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Hierarchies”, Funct. Anal. Appl., 37:2 (2003), 103–113  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. O. I. Mokhov, “Systems of integrals in involution and associativity equations”, Russian Math. Surveys, 61:3 (2006), 568–570  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. Kupershmidt B.A., “Noncommutative integrable systems of hydrodynamic type”, Acta Applicandae Mathematicae, 92:3 (2006), 269–292  crossref  mathscinet  zmath  isi  scopus  scopus
    16. Kupershmidt B.A., “Hydrodynamical chains of Pavlov class”, Physics Letters A, 356:2 (2006), 115–118  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    17. Kupershmidt B., “Left–Symmetric algebras in hydrodynamics”, Letters in Mathematical Physics, 76:1 (2006), 1–18  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    18. Ferapontov E.V., Khusnutdinova K.R., Tsarev S.P., “On a class of three–dimensional integrable Lagrangians”, Communications in Mathematical Physics, 261:1 (2006), 225–243  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    19. M. V. Pavlov, “Integrability of the Egorov systems of hydrodynamic type”, Theoret. and Math. Phys., 150:2 (2007), 225–243  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. Abenda S., Grava T., “Reciprocal transformations and flat metrics on Hurwitz spaces”, Journal of Physics A–Mathematical and Theoretical, 40:35 (2007), 10769–10790  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    21. O. I. Mokhov, “Realization of Frobenius Manifolds as Submanifolds in Pseudo-Euclidean Spaces”, Proc. Steklov Inst. Math., 267 (2009), 217–234  mathnet  crossref  mathscinet  zmath  isi  elib
    22. Sergyeyev A., “Infinite hierarchies of nonlocal symmetries of the Chen–Kontsevich–Schwarz type for the oriented associativity equations”, Journal of Physics A–Mathematical and Theoretical, 42:40 (2009), 404017  crossref  mathscinet  zmath  isi  scopus  scopus
    23. O. I. Mokhov, “Pencils of compatible metrics and integrable systems”, Russian Math. Surveys, 72:5 (2017), 889–937  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    24. Prykarpatski A.K., “On the Solutions to the Witten-Dijkgraaf-Verlinde-Verlinde Associativity Equations and Their Algebraic Properties”, J. Geom. Phys., 134 (2018), 77–83  crossref  mathscinet  zmath  isi  scopus
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