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Mokhov, Oleg Ivanovich

Statistics Math-Net.Ru
Total publications: 60
Scientific articles: 59
Presentations: 10

Number of views:
This page:8968
Abstract pages:21971
Full texts:7849
References:2172
Senior Researcher
Doctor of physico-mathematical sciences (1996)
Speciality: 01.01.04 (Geometry and topology)
Birth date: 28.06.1959
Phone: +7 (499) 124 13 59
E-mail: , ,
Keywords: differential geometry, mathematical physics, integrable systems, Poisson geometry, symplectic geometry, algebraic geometry, Riemannian geometry, nonlinear equations, systems of hydrodynamic type, discrete geometry, discrete equations, Hamiltonian and bi-Hamiltonian systems, commuting differential operators.
UDC: 512.7, 514.7, 517.9, 517.91, 512.643.2, 511.9, 514.74, 514.174.6, 517.957, 514.8, 517.958, 517.95, 512.55
MSC: 37J05, 53D05

Subject:

Symplectic geometry, Poisson geometry, algebraic geometry, differential geometry and Riemannian geometry, nonlinear equations of mathematical physics, integrable systems, Hamiltonian and bi-Hamiltonian systems, discrete geometry and discrete equations, systems of hydrodynamic type, commuting differential operators.

   
Main publications:
  1. O. I. Mokhov, Symplectic and Poisson geometry on loop spaces of smooth manifolds and integrable equations, Reviews in Mathematics and Mathematical Physics, 11, part 2, eds. S. P. Novikov and I. M. Krichever, Harwood Academic Publishers, Amsterdam, 2001, 204  mathscinet  zmath
  2. O. I. Mokhov, “Soglasovannye i pochti soglasovannye psevdorimanovy metriki”, Funktsionalnyi analiz i ego prilozheniya, 35:2 (2001), 24–36  mathnet  mathscinet  zmath
  3. O. I. Mokhov, “Simplekticheskie i puassonovy struktury na prostranstvakh petel gladkikh mnogoobrazii i integriruemye sistemy”, Uspekhi matematicheskikh nauk, 53:3 (1998), 85–192  mathnet  mathscinet  zmath
  4. O. I. Mokhov, “O gruppakh kogomologii kompleksov odnorodnykh form na prostranstvakh petel gladkikh mnogoobrazii”, Funktsionalnyi analiz i ego prilozheniya, 32:3 (1998), 22–34  mathnet  mathscinet  zmath
  5. O. I. Mokhov, “Kommutiruyuschie differentsialnye operatory ranga 3 i nelineinye uravneniya”, Izvestiya AN SSSR, seriya matematicheskaya, 53:6 (1989), 1291–1315  mathnet  mathscinet  zmath

http://www.mathnet.ru/eng/person8947
http://scholar.google.com/citations?user=b3C7Zo0AAAAJ&hl=en
http://zbmath.org/authors/?q=ai:mokhov.oleg-i
https://mathscinet.ams.org/mathscinet/MRAuthorID/211830
http://elibrary.ru/author_items.asp?spin=3128-4327
ISTINA http://istina.msu.ru/workers/843956
http://orcid.org/0000-0002-9367-8405
http://www.researcherid.com/rid/B-6678-2013
http://www.scopus.com/authid/detail.url?authorId=7004444589
https://www.researchgate.net/profile/Oleg_Mokhov
https://arxiv.org/a/mokhov_o_1

Publications in Math-Net.Ru
2020
1. E. V. Glukhov, O. I. Mokhov, “On algebraic-geometry methods for constructing submanifolds with flat normal bundle and holonomic net of curvature lines”, Funktsional. Anal. i Prilozhen., 54:3 (2020),  26–37  mathnet
2019
2. E. V. Glukhov, O. I. Mokhov, “On algebraic-geometry methods for constructing flat diagonal metrics of a special form”, Uspekhi Mat. Nauk, 74:4(448) (2019),  185–186  mathnet  elib; Russian Math. Surveys, 74:4 (2019), 761–763  isi
3. O. I. Mokhov, N. A. Strizhova, “Liouville integrability of the reduction of the associativity equations on the set of stationary points of an integral in the case of three primary fields”, Uspekhi Mat. Nauk, 74:2(446) (2019),  191–192  mathnet  elib; Russian Math. Surveys, 74:2 (2019), 369–371  isi  scopus
2018
4. O. I. Mokhov, N. A. Strizhova, “Classification of the associativity equations possessing a Hamiltonian structure of Dubrovin–Novikov type”, Uspekhi Mat. Nauk, 73:1(439) (2018),  183–184  mathnet  mathscinet  elib; Russian Math. Surveys, 73:1 (2018), 175–177  isi  scopus
5. O. I. Mokhov, N. A. Pavlenko, “Classification of the associativity equations with a first-order Hamiltonian operator”, TMF, 197:1 (2018),  124–137  mathnet  elib; Theoret. and Math. Phys., 197:1 (2018), 1501–1513  isi  scopus
2017
6. O. I. Mokhov, “Pencils of compatible metrics and integrable systems”, Uspekhi Mat. Nauk, 72:5(437) (2017),  113–164  mathnet  mathscinet  elib; Russian Math. Surveys, 72:5 (2017), 889–937  isi  scopus
2016
7. O. I. Mokhov, “On metrics of diagonal curvature”, Fundam. Prikl. Mat., 21:6 (2016),  171–182  mathnet
2013
8. O. I. Mokhov, “On Commutative Subalgebras of the Weyl Algebra Related to Commuting Operators of Arbitrary Rank and Genus”, Mat. Zametki, 94:2 (2013),  314–316  mathnet  mathscinet  zmath  elib; Math. Notes, 94:2 (2013), 298–300  isi  elib  scopus
2011
9. O. I. Mokhov, “Deformations of Poisson Structures by Closed $3$-Forms”, Mat. Zametki, 89:6 (2011),  944–947  mathnet  mathscinet; Math. Notes, 89:6 (2011), 899–902  isi  scopus
10. Oleg I. Mokhov, “On Initial Data in the Problem of Consistency on Cubic Lattices for $3\times3$ Determinants”, SIGMA, 7 (2011), 075, 19 pp.  mathnet  mathscinet  isi  scopus
11. O. I. Mokhov, “Compatible metrics and the diagonalizability of nonlocally bi-Hamiltonian systems of hydrodynamic type”, TMF, 167:1 (2011),  3–22  mathnet  mathscinet; Theoret. and Math. Phys., 167:1 (2011), 403–420  isi  scopus
2010
12. O. I. Mokhov, “Riemann invariants of semisimple non-locally bi-Hamiltonian systems of hydrodynamic type and compatible metrics”, Uspekhi Mat. Nauk, 65:6(396) (2010),  189–190  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 65:6 (2010), 1183–1185  isi  elib  scopus
2009
13. O. I. Mokhov, “Realization of Frobenius Manifolds as Submanifolds in Pseudo-Euclidean Spaces”, Tr. Mat. Inst. Steklova, 267 (2009),  226–244  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 267 (2009), 217–234  isi  scopus
14. O. I. Mokhov, “Consistency on Cubic Lattices for Determinants of Arbitrary Orders”, Tr. Mat. Inst. Steklova, 266 (2009),  202–217  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 266 (2009), 195–209  isi  elib  scopus
2008
15. O. I. Mokhov, “The Classification of Nonsingular Multidimensional Dubrovin–Novikov Brackets”, Funktsional. Anal. i Prilozhen., 42:1 (2008),  39–52  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 42:1 (2008), 33–44  isi  elib  scopus
16. O. I. Mokhov, “On consistency of determinants on cubic lattices”, Uspekhi Mat. Nauk, 63:6(384) (2008),  169–170  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:6 (2008), 1146–1148  isi  elib  scopus
17. O. I. Mokhov, “Duality in a special class of submanifolds and Frobenius manifolds”, Uspekhi Mat. Nauk, 63:2(380) (2008),  177–178  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:2 (2008), 378–380  isi  scopus
2007
18. O. I. Mokhov, “Theory of submanifolds, associativity equations in 2D topological quantum field theories, and Frobenius manifolds”, TMF, 152:2 (2007),  368–376  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 152:2 (2007), 1183–1190  isi  scopus
2006
19. O. I. Mokhov, “Nonlocal Hamiltonian Operators of Hydrodynamic Type with Flat Metrics, Integrable Hierarchies, and the Associativity Equations”, Funktsional. Anal. i Prilozhen., 40:1 (2006),  14–29  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 40:1 (2006), 11–23  isi  elib  scopus
20. O. I. Mokhov, “Systems of integrals in involution and associativity equations”, Uspekhi Mat. Nauk, 61:3(369) (2006),  175–176  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 61:3 (2006), 568–570  isi  elib  scopus
21. O. I. Mokhov, “The classification of multidimensional Poisson brackets of hydrodynamic type”, Uspekhi Mat. Nauk, 61:2(368) (2006),  167–168  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 61:2 (2006), 356–358  isi  elib  scopus
2004
22. O. I. Mokhov, “Non-local Hamiltonian operators of hydrodynamic type with flat metrics, and the associativity equations”, Uspekhi Mat. Nauk, 59:1(355) (2004),  187–188  mathnet  mathscinet  zmath; Russian Math. Surveys, 59:1 (2004), 191–192  isi  scopus
23. O. I. Mokhov, “Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamй Equations”, TMF, 138:2 (2004),  283–296  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 138:2 (2004), 238–249  isi
2003
24. O. I. Mokhov, “The Liouville Canonical Form for Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Hierarchies”, Funktsional. Anal. i Prilozhen., 37:2 (2003),  28–40  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 37:2 (2003), 103–113  isi  scopus
25. O. I. Mokhov, “Quasi-Frobenius Algebras and Their Integrable $N$-Parameter Deformations Generated by Compatible $(N\times N)$ Metrics of Constant Riemannian Curvature”, TMF, 136:1 (2003),  20–29  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 136:1 (2003), 908–916  isi
2002
26. O. I. Mokhov, “Compatible Metrics of Constant Riemannian Curvature: Local Geometry, Nonlinear Equations, and Integrability”, Funktsional. Anal. i Prilozhen., 36:3 (2002),  36–47  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 36:3 (2002), 196–204  isi  scopus
27. O. I. Mokhov, “Lax pairs for compatible non-local Hamiltonian operators of hydrodynamic type”, Uspekhi Mat. Nauk, 57:6(348) (2002),  189–190  mathnet  mathscinet  zmath; Russian Math. Surveys, 57:6 (2002), 1234–1235  isi  scopus
28. O. I. Mokhov, “Integrable bi-Hamiltonian hierarchies generated by compatible metrics of constant Riemannian curvature”, Uspekhi Mat. Nauk, 57:5(347) (2002),  157–158  mathnet  mathscinet  zmath; Russian Math. Surveys, 57:5 (2002), 999–1001  isi  scopus
29. O. I. Mokhov, “The Lax pair for non-singular pencils of metrics of constant Riemannian curvature”, Uspekhi Mat. Nauk, 57:3(345) (2002),  155–156  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 57:3 (2002), 603–605  isi  scopus
30. O. I. Mokhov, “Integrable bi-Hamiltonian systems of hydrodynamic type”, Uspekhi Mat. Nauk, 57:1(343) (2002),  157–158  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 57:1 (2002), 153–154  isi  scopus
31. O. I. Mokhov, “Compatible Dubrovin–Novikov Hamiltonian Operators, Lie Derivative, and Integrable Systems of Hydrodynamic Type”, TMF, 133:2 (2002),  279–288  mathnet  mathscinet  elib; Theoret. and Math. Phys., 133:2 (2002), 1557–1564  isi
32. O. I. Mokhov, “Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Hierarchies Related to Them”, TMF, 132:1 (2002),  60–73  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 132:1 (2002), 942–954  isi
33. O. I. Mokhov, “Integrability of the Equations for Nonsingular Pairs of Compatible Flat Metrics”, TMF, 130:2 (2002),  233–250  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 130:2 (2002), 198–212  isi
2001
34. O. I. Mokhov, “Compatible and Almost Compatible Pseudo-Riemannian Metrics”, Funktsional. Anal. i Prilozhen., 35:2 (2001),  24–36  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 35:2 (2001), 100–110  isi  scopus
35. O. I. Mokhov, “Compatible Dubrovin–Novikov Hamiltonian operators and the Lie derivative”, Uspekhi Mat. Nauk, 56:6(342) (2001),  161–162  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 56:6 (2001), 1175–1176  isi  scopus
36. O. I. Mokhov, “Flat pencils of metrics and integrable reductions of Lamé's equations”, Uspekhi Mat. Nauk, 56:2(338) (2001),  221–222  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 56:2 (2001), 416–418  isi  scopus
2000
37. O. I. Mokhov, “Compatible and almost compatible metrics”, Uspekhi Mat. Nauk, 55:4(334) (2000),  217–218  mathnet  mathscinet  zmath; Russian Math. Surveys, 55:4 (2000), 819–821  isi  scopus
1999
38. O. I. Mokhov, “Compatible Poisson Structures of Hydrodynamic Type and Associativity Equations”, Tr. Mat. Inst. Steklova, 225 (1999),  284–300  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 225 (1999), 269–284
1998
39. O. I. Mokhov, “On the Cohomology Groups of Complexes of Homogeneous Forms on Loop Spaces of Smooth Manifolds”, Funktsional. Anal. i Prilozhen., 32:3 (1998),  22–34  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 32:3 (1998), 162–171  isi
40. O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Uspekhi Mat. Nauk, 53:3(321) (1998),  85–192  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 53:3 (1998), 515–622  isi  elib  scopus
41. O. I. Mokhov, “On compatible potential deformations of Frobenius algebras and associativity equations”, Uspekhi Mat. Nauk, 53:2(320) (1998),  153–154  mathnet  mathscinet  zmath; Russian Math. Surveys, 53:2 (1998), 396–397  isi  scopus
1997
42. O. I. Mokhov, “On compatible Poisson structures of hydrodynamic type”, Uspekhi Mat. Nauk, 52:6(318) (1997),  171–172  mathnet  mathscinet; Russian Math. Surveys, 52:6 (1997), 1310–1311  isi  scopus
43. O. I. Mokhov, “Differential geometry of symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Tr. Mat. Inst. Steklova, 217 (1997),  100–134  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 217 (1997), 91–125
1996
44. O. I. Mokhov, E. V. Ferapontov, “The Associativity Equations in the Two-Dimensional Topological Field Theory as Integrable Hamiltonian Nondiagonalizable Systems of Hydrodynamic Type”, Funktsional. Anal. i Prilozhen., 30:3 (1996),  62–72  mathnet  mathscinet  zmath; Funct. Anal. Appl., 30:3 (1996), 195–203  isi
45. O. I. Mokhov, “Complex homogeneous forms on loop spaces of smooth manifolds and their cohomology groups”, Uspekhi Mat. Nauk, 51:2(308) (1996),  141–142  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:2 (1996), 341–342  isi  scopus
1994
46. O. I. Mokhov, E. V. Ferapontov, “Hamiltonian Pairs Associated with Skew-Symmetric Killing Tensors on Spaces of Constant Curvature”, Funktsional. Anal. i Prilozhen., 28:2 (1994),  60–63  mathnet  mathscinet  zmath; Funct. Anal. Appl., 28:2 (1994), 123–125  isi
1991
47. O. I. Mokhov, “Homogeneous symplectic structures of second order on loop spaces and symplectic connections”, Funktsional. Anal. i Prilozhen., 25:2 (1991),  65–67  mathnet  mathscinet  zmath; Funct. Anal. Appl., 25:2 (1991), 136–137  isi
48. O. I. Mokhov, “Canonical Hamiltonian representation of the Krichever–Novikov equation”, Mat. Zametki, 50:3 (1991),  87–96  mathnet  mathscinet  zmath; Math. Notes, 50:3 (1991), 939–945  isi
1990
49. O. I. Mokhov, “Симплектические формы на пространстве петель и риманова геометрия”, Funktsional. Anal. i Prilozhen., 24:3 (1990),  86–87  mathnet  mathscinet  zmath; Funct. Anal. Appl., 24:3 (1990), 247–249  isi
50. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 45:3 (1990), 218–219  isi
51. O. I. Mokhov, “A Hamiltonian structure of evolution in the space variable $x$ for the Korteweg–de Vries equation”, Uspekhi Mat. Nauk, 45:1(271) (1990),  181–182  mathnet  mathscinet  zmath; Russian Math. Surveys, 45:1 (1990), 218–220  isi
1989
52. O. I. Mokhov, “Commuting differential operators of rank 3, and nonlinear differential equations”, Izv. Akad. Nauk SSSR Ser. Mat., 53:6 (1989),  1291–1315  mathnet  mathscinet  zmath; Math. USSR-Izv., 35:3 (1990), 629–655
53. O. I. Mokhov, “Canonical variables for the two-dimensional hydrodynamics of an incompressible fluid with vorticity”, TMF, 78:1 (1989),  136–139  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 78:1 (1989), 97–99  isi
1988
54. O. I. Mokhov, “Dubrovin–Novikov type Poisson brackets (DN-brackets)”, Funktsional. Anal. i Prilozhen., 22:4 (1988),  92–93  mathnet  mathscinet  zmath; Funct. Anal. Appl., 22:4 (1998), 336–338
1987
55. O. I. Mokhov, “Hamiltonian differential operators and contact geometry”, Funktsional. Anal. i Prilozhen., 21:3 (1987),  53–60  mathnet  mathscinet  zmath; Funct. Anal. Appl., 21:3 (1987), 217–223  isi
56. O. I. Mokhov, “On the Hamiltonian property of an arbitrary evolution system on the set of stationary points of its integral”, Izv. Akad. Nauk SSSR Ser. Mat., 51:6 (1987),  1345–1352  mathnet  mathscinet  zmath; Math. USSR-Izv., 31:3 (1988), 657–664
1985
57. O. I. Mokhov, “Local third-order Poisson brackets”, Uspekhi Mat. Nauk, 40:5(245) (1985),  257–258  mathnet  mathscinet  zmath; Russian Math. Surveys, 40:5 (1985), 233–234
1984
58. O. I. Mokhov, “The Hamiltonian property of an evolutionary flow on the set of stationary points of its integral”, Uspekhi Mat. Nauk, 39:4(238) (1984),  173–174  mathnet  mathscinet  zmath; Russian Math. Surveys, 39:4 (1984), 133–134  isi
1982
59. O. I. Mokhov, “Commuting ordinary differential operators of rank 3 corresponding to an elliptic curve”, Uspekhi Mat. Nauk, 37:4(226) (1982),  169–170  mathnet  mathscinet  zmath; Russian Math. Surveys, 37:4 (1982), 129–130  isi

1995
60. O. I. Mokhov, S. P. Novikov, A. K. Pogrebkov, “Irina Yakovlevna Dorfman (obituary)”, Uspekhi Mat. Nauk, 50:6(306) (1995),  151–156  mathnet  mathscinet  zmath; Russian Math. Surveys, 50:6 (1995), 1241–1246  isi

Presentations in Math-Net.Ru
1. Метрики диагональной кривизны
O. I. Mokhov
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
April 19, 2017 18:30
2. Commuting ordinary differential operators of arbitrary genus and arbitrary rank with polynomial coefficients
O. I. Mokhov
International conference "Geometry, Topology, Integrable Systems" in honour of S. P. Novikovs 75th birthday
June 17, 2013 16:50   
3. On Hamiltonian geometry of the associativity equations
O. I. Mokhov, N. Pavlenko
International Workshop «Geometric Structures in Integrable Systems»
October 30, 2012 14:40   
4. Коммутирующие обыкновенные дифференциальные операторы ранга 4, отвечающие эллиптической кривой II
O. I. Mokhov
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
November 9, 2011 18:30
5. Коммутирующие обыкновенные дифференциальные операторы ранга 4, отвечающие эллиптической кривой
O. I. Mokhov
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
November 2, 2011 18:30
6. Согласованные метрики и римановы инварианты. II
O. I. Mokhov
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
November 3, 2010 18:30
7. Согласованные метрики и римановы инварианты. I
O. I. Mokhov
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
October 27, 2010 18:30
8. Совместность на кубических решетках детерминантов произвольных порядков
O. I. Mokhov
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
March 4, 2009
9. О двойственности в специальном классе многообразий
O. I. Mokhov
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
April 30, 2008
10. Плоские подмногообразия с плоской нормальной связностью, уравнения ассоциативности и фробениусовы структуры
O. I. Mokhov
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
November 10, 2004

Organisations
 
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