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

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

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
\Bibitem{MokFer90} \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 \mathnet{http://mi.mathnet.ru/umn4744} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1071942} \zmath{https://zbmath.org/?q=an:0712.35080} \transl \jour Russian Math. Surveys \yr 1990 \vol 45 \issue 3 \pages 218--219 \crossref{https://doi.org/10.1070/RM1990v045n03ABEH002351} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990EZ60500006} 

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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, “Differential geometry of nonlocal Hamiltonian operators of hydrodynamic type”, Funct. Anal. Appl., 25:3 (1991), 195–204
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
3. E. V. Ferapontov, “Nonlocal matrix hamiltonian operators, differential geometry, and applications”, Theoret. and Math. Phys., 91:3 (1992), 642–649
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
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
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
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
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
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
10. A. Ya. Mal'tsev, “Non-local Poisson brackets and Whitham's method”, Russian Math. Surveys, 54:6 (1999), 1252–1253
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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
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24. Lorenzoni, P, “A bi-Hamiltonian approach to the sine-Gordon and Liouville hierarchies”, Letters in Mathematical Physics, 67:2 (2004), 83
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
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36. Bogoyavlenskij O.I., Reynolds A.P., “Criteria for Existence of a Hamiltonian Structure”, Regular & Chaotic Dynamics, 15:4–5 (2010), 431–439
37. I. A. Taimanov, “Singular spectral curves in finite-gap integration”, Russian Math. Surveys, 66:1 (2011), 107–144
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
39. D. A. Berdinskii, I. P. Rybnikov, “On orthogonal curvilinear coordinate systems in constant curvature spaces”, Siberian Math. J., 52:3 (2011), 394–401
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