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Funktsional. Anal. i Prilozhen., 1991, Volume 25, Issue 3, Pages 37–49 (Mi faa879)  

This article is cited in 40 scientific papers (total in 40 papers)

Differential geometry of nonlocal Hamiltonian operators of hydrodynamic type

E. V. Ferapontov

Computing Centre, USSR Academy of Sciences

Full text: PDF file (1538 kB)
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English version:
Functional Analysis and Its Applications, 1991, 25:3, 195–204

Bibliographic databases:

UDC: 514.8
Received: 29.08.1990

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://www.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}
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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. E. V. Ferapontov, “Dirac reduction of the hamiltonian operator $\delta^{IJ}\frac{d}{dx}$ to a submanifold of euclidean space with flat normal connection”, Funct. Anal. Appl., 26:4 (1992), 298–300  mathnet  crossref  mathscinet  zmath  isi
    2. E. V. Ferapontov, “Nonlocal matrix hamiltonian operators, differential geometry, and applications”, Theoret. and Math. Phys., 91:3 (1992), 642–649  mathnet  crossref  mathscinet  zmath  isi
    3. M. V. Pavlov, “Discrete symmetry and local Hamiltonian structures of systems of hydrodynamical type”, Russian Math. Surveys, 48:6 (1993), 178–180  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. O. I. Mokhov, E. V. Ferapontov, “Hamiltonian Pairs Associated with Skew-Symmetric Killing Tensors on Spaces of Constant Curvature”, Funct. Anal. Appl., 28:2 (1994), 123–125  mathnet  crossref  mathscinet  zmath  isi
    5. E. V. Ferapontov, “Conformally plane metrics, systems of hydrodynamic type, and non-local Hamiltonian operators”, Russian Math. Surveys, 50:4 (1995), 811–813  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. V. L. Alekseev, “On non-local Hamiltonian operators of hydrodynamic type connected with Whitham's equations”, Russian Math. Surveys, 50:6 (1995), 1253–1255  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. O. I. Mokhov, E. V. Ferapontov, “The Associativity Equations in the Two-Dimensional Topological Field Theory as Integrable Hamiltonian Nondiagonalizable Systems of Hydrodynamic Type”, Funct. Anal. Appl., 30:3 (1996), 195–203  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Ferapontov, EV, “Bi-Hamiltonian structure of equations of associativity in 2-d topological field theory”, Communications in Mathematical Physics, 186:3 (1997), 649  crossref  mathscinet  zmath  adsnasa  isi
    9. O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Russian Math. Surveys, 53:3 (1998), 515–622  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. O. I. Mokhov, “On the Cohomology Groups of Complexes of Homogeneous Forms on Loop Spaces of Smooth Manifolds”, Funct. Anal. Appl., 32:3 (1998), 162–171  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. L. V. Bogdanov, E. V. Ferapontov, “A nonlocal Hamiltonian formalism for semi-Hamiltonian systems of the hydrodynamic type”, Theoret. and Math. Phys., 116:1 (1998), 829–835  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. O. I. Mokhov, “Compatible and almost compatible metrics”, Russian Math. Surveys, 55:4 (2000), 819–821  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    13. 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
    14. O. I. Mokhov, “Lax pairs for compatible non-local Hamiltonian operators of hydrodynamic type”, Russian Math. Surveys, 57:6 (2002), 1234–1235  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    15. 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
    16. 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
    17. 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
    18. M. V. Pavlov, S. P. Tsarev, “Tri-Hamiltonian Structures of Egorov Systems of Hydrodynamic Type”, Funct. Anal. Appl., 37:1 (2003), 32–45  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. 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
    20. O. I. Mokhov, “Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamй Equations”, Theoret. and Math. Phys., 138:2 (2004), 238–249  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    21. M. V. Pavlov, “The Boussinesq equation and Miura type transformations”, J. Math. Sci., 136:6 (2006), 4478–4483  mathnet  crossref  mathscinet  zmath
    22. O. I. Mokhov, “Non-local Hamiltonian operators of hydrodynamic type with flat metrics, and the associativity equations”, Russian Math. Surveys, 59:1 (2004), 191–192  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    23. M. V. Pavlov, “The description of pairs of compatible first-order differential geometric poisson brackets”, Theoret. and Math. Phys., 142:2 (2005), 244–258  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    24. O. I. Mokhov, “Nonlocal Hamiltonian Operators of Hydrodynamic Type with Flat Metrics, Integrable Hierarchies, and the Associativity Equations”, Funct. Anal. Appl., 40:1 (2006), 11–23  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    25. Artur Sergyeyev, “Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility”, SIGMA, 3 (2007), 062, 14 pp.  mathnet  crossref  mathscinet  zmath
    26. A. Ya. Maltsev, “The Lorentz-Invariant Deformation of the Whitham System for the Nonlinear Klein–Gordon Equation”, Funct. Anal. Appl., 42:2 (2008), 103–115  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    27. Victor D. Gershun, “Integrable String Models in Terms of Chiral Invariants of $\mathrm{SU}(n)$, $\mathrm{SO}(n)$, $\mathrm{SP}(n)$ Groups”, SIGMA, 4 (2008), 041, 16 pp.  mathnet  crossref  mathscinet  zmath
    28. O. I. Mokhov, “Riemann invariants of semisimple non-locally bi-Hamiltonian systems of hydrodynamic type and compatible metrics”, Russian Math. Surveys, 65:6 (2010), 1183–1185  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    29. Gibbons J., Lorenzoni P., Raimondo A., “Purely nonlocal Hamiltonian formalism for systems of hydrodynamic type”, J Geom Phys, 60:9 (2010), 1112–1126  crossref  isi
    30. O. I. Mokhov, “Compatible metrics and the diagonalizability of nonlocally bi-Hamiltonian systems of hydrodynamic type”, Theoret. and Math. Phys., 167:1 (2011), 403–420  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    31. Andrei Ya. Maltsev, “Whitham's Method and Dubrovin–Novikov Bracket in Single-Phase and Multiphase Cases”, SIGMA, 8 (2012), 103, 54 pp.  mathnet  crossref
    32. Maltsev A.Ya., “The Multi-Dimensional Hamiltonian Structures in the Whitham Method”, J. Math. Phys., 54:5 (2013), 053507  crossref  isi
    33. Cirilo-Lombardo D.J., “Integrable Hydrodynamic Equations For Initial Chiral Currents and Infinite Hydrodynamic Chains From WZNW Model and String Model of WZNW Type With Su(2), So(3), Sp(2), Su(Infinity), So(Infinity), Sp(Infinity) Constant Torsions”, Int. J. Mod. Phys. A, 29:24 (2014), 1450134  crossref  isi
    34. 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
    35. 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
    36. Della Vedova A., Lorenzoni P., Savoldi A., “Deformations of non-semisimple Poisson pencils of hydrodynamic type”, Nonlinearity, 29:9 (2016), 2715–2754  crossref  mathscinet  zmath  isi  scopus
    37. Maltsev A.Ya., “On the canonical forms of the multi-dimensional averaged Poisson brackets”, J. Math. Phys., 57:5 (2016), 053501  crossref  mathscinet  zmath  isi  elib  scopus
    38. O. I. Mokhov, “O metrikakh diagonalnoi krivizny”, Fundament. i prikl. matem., 21:6 (2016), 171–182  mathnet
    39. 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
    40. Bulchandani V.B., “On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems”, J. Phys. A-Math. Theor., 50:43 (2017), 435203  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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