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Uspekhi Mat. Nauk, 1990, Volume 45, Issue 3(273), Pages 191–192 (Mi umn4744)  

This article is cited in 46 scientific papers (total in 46 papers)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

Non-local Hamiltonian operators of hydrodynamic type related to metrics of constant curvature

O. I. Mokhova, E. V. Ferapontovb

a All-Russian Scientific Research Institute of Physical-Technical and Radiotechnical Measurements
b Dorodnitsyn Computing Centre of the Russian Academy of Sciences

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English version:
Russian Mathematical Surveys, 1990, 45:3, 218–219

Bibliographic databases:

MSC: 70Hxx, 47Axx
Received: 12.12.1989

Citation: O. I. Mokhov, E. V. Ferapontov, “Non-local Hamiltonian operators of hydrodynamic type related to metrics of constant curvature”, Uspekhi Mat. Nauk, 45:3(273) (1990), 191–192; Russian Math. Surveys, 45:3 (1990), 218–219

Citation in format AMSBIB
\by O.~I.~Mokhov, E.~V.~Ferapontov
\paper Non-local Hamiltonian operators of hydrodynamic type related to metrics of constant curvature
\jour Uspekhi Mat. Nauk
\yr 1990
\vol 45
\issue 3(273)
\pages 191--192
\jour Russian Math. Surveys
\yr 1990
\vol 45
\issue 3
\pages 218--219

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    This publication is cited in the following articles:
    1. E. V. Ferapontov, “Differential geometry of nonlocal Hamiltonian operators of hydrodynamic type”, Funct. Anal. Appl., 25:3 (1991), 195–204  mathnet  crossref  mathscinet  zmath  isi
    2. 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
    3. 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
    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. 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
    6. 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
    7. 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
    8. 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
    9. 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
    10. A. Ya. Mal'tsev, “Non-local Poisson brackets and Whitham's method”, Russian Math. Surveys, 54:6 (1999), 1252–1253  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    11. O. I. Mokhov, “Compatible and almost compatible metrics”, Russian Math. Surveys, 55:4 (2000), 819–821  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    12. 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
    13. Maltsev A.Ya., Novikov S.P., “On the local systems Hamiltonian in the weakly non-local Poisson brackets”, Physica D, 156:1-2 (2001), 53–80  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. O. I. Mokhov, “Compatible Metrics of Constant Riemannian Curvature: Local Geometry, Nonlinear Equations, and Integrability”, Funct. Anal. Appl., 36:3 (2002), 196–204  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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. O. I. Mokhov, “The Lax pair for non-singular pencils of metrics of constant Riemannian curvature”, Russian Math. Surveys, 57:3 (2002), 603–605  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    19. 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
    20. 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
    21. 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
    22. 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
    23. 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
    24. Lorenzoni, P, “A bi-Hamiltonian approach to the sine-Gordon and Liouville hierarchies”, Letters in Mathematical Physics, 67:2 (2004), 83  crossref  mathscinet  zmath  adsnasa  isi  elib
    25. Maltsev, AY, “Weakly nonlocal symplectic structures, Whitham method and weakly nonlocal symplectic structures of hydrodynamic type”, Journal of Physics A-Mathematical and General, 38:3 (2005), 637  crossref  mathscinet  zmath  adsnasa  isi  elib
    26. Maxim V. Pavlov, “The Kupershmidt hydrodynamic chains and lattices”, Internat Math Res Notices, 2006 (2006), 1  crossref  mathscinet
    27. 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
    28. Maltsev, AY, “Whitham systems and deformations”, Journal of Mathematical Physics, 47:7 (2006), 073505  crossref  mathscinet  zmath  adsnasa  isi
    29. Maxim V. Pavlov, “Algebro-Geometric Approach in the Theory of Integrable Hydrodynamic Type Systems”, Comm Math Phys, 272:2 (2007), 469  crossref  mathscinet  zmath  isi  elib
    30. 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
    31. Bogoyavlenskij, O, “Form-invariant Poisson brackets of hydrodynamic type with several spatial variables”, Journal of Mathematical Physics, 49:5 (2008), 053520  crossref  mathscinet  zmath  adsnasa  isi  elib
    32. 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
    33. 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
    34. John Gibbons, Paolo Lorenzoni, Andrea Raimondo, “Purely nonlocal Hamiltonian formalism for systems of hydrodynamic type”, Journal of Geometry and Physics, 60:9 (2010), 1112  crossref
    35. Maltsev A.Ya., “The conservation of the Hamiltonian structures in the deformations of the Whitham systems”, Journal of Physics a-Mathematical and Theoretical, 43:6 (2010), 065202  crossref  isi
    36. Bogoyavlenskij O.I., Reynolds A.P., “Criteria for Existence of a Hamiltonian Structure”, Regular & Chaotic Dynamics, 15:4–5 (2010), 431–439  crossref  isi
    37. I. A. Taimanov, “Singular spectral curves in finite-gap integration”, Russian Math. Surveys, 66:1 (2011), 107–144  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    38. 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
    39. D. A. Berdinskii, I. P. Rybnikov, “On orthogonal curvilinear coordinate systems in constant curvature spaces”, Siberian Math. J., 52:3 (2011), 394–401  mathnet  crossref  mathscinet  isi
    40. Misha Bialy, Andrey Mironov, “New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces”, centr.eur.j.math, 2012  crossref
    41. Misha Bialy, A.E.. Mironov, “Integrable geodesic flows on 2-torus: Formal solutions and variational principle”, Journal of Geometry and Physics, 2014  crossref
    42. 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
    43. A. Ya. Maltsev, “On the minimal set of conservation laws and the Hamiltonian structure of the Whitham equations”, J. Math. Phys, 56:2 (2015), 023510  crossref
    44. 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
    45. O. I. Mokhov, “O metrikakh diagonalnoi krivizny”, Fundament. i prikl. matem., 21:6 (2016), 171–182  mathnet
    46. 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
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