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Marchuk, Nikolay Gur'evich

Total publications: 61 (61)
in MathSciNet: 37 (37)
in zbMATH: 26 (26)
in Web of Science: 42 (42)
in Scopus: 30 (30)
Cited articles: 31
Citations in Math-Net.Ru: 20
Citations in MathSciNet: 32
Citations in Web of Science: 102
Citations in Scopus: 106
Presentations: 8

Number of views:
This page:3569
Abstract pages:1534
Full texts:423
References:156
Marchuk, Nikolay Gur'evich
Doctor of physico-mathematical sciences
Speciality: 01.01.03 (Mathematical physics)
Birth date: 16.10.1955
Phone: +7 (495) 984 81 41 * 39 12, +7(916) 184 50 25
E-mail: ,
Website: http://www.mi.ras.ru/~nmarchuk
Keywords: hyperbolic equations, gauge symmetry, Dirac equation, Dirac–Yang–Mills equations, pseudo-unitary symmetry.
UDC: 517.958

Subject:

Relativistic equations of quandum physics. Dirac equation. Yang–Mills equation. Einstein equation. Clifford algebras and differential forms.

Biography

I graduated from the Novosibirsk State University in 1977. My Ph.D. thesis was completed under the guidance of the world famous Academician Prof. S.K. Godunov and was dedicated to investigation of some initial-boundary value problems for the hyperbolic differential equations. After Ph.D. (1980) I was invited to work in the Steklov Mathematical Institute of the Russian Academy of Sciences.

Fields of interest Presently my scientific interests lie in investigating some mathematical problems of modern physics (Dirac equation, Yang–Mills equations, gauge fields, the gravitational field). Among others, my favorite mathematical tools are differential forms and Clifford Algebra.

   
Main publications:
  1. N. Marchuk, Field theory equations, Amazon, CreateSpace, 2012 , 290 pp.
  2. N. G. Marchuk, D. S. Shirokov, Vvedenie v teoriyu algebr Klifforda, Fazis, Moskva, 2012 , 590 pp.
  3. N. G. Marchuk, Uravneniya teorii polya i algebry Klifforda, RKhD, Izhevsk, 2009 , 304 pp.

http://www.mathnet.ru/eng/person18563
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:marchuk.nikolaj-gurevich
https://mathscinet.ams.org/mathscinet/MRAuthorID/203675
http://elibrary.ru/author_items.asp?authorid=14076
http://www.researcherid.com/rid/J-6168-2013
http://www.scopus.com/authid/detail.url?authorId=6602450293

Full list of scientific publications:
| by years | by types | by times cited in WoS | by times cited in Scopus | scientific publications | common list |



   2019
1. N. G. Marchuk, Mathematical physics and applications, Collected papers. In commemoration of the 95th anniversary of Academician Vasilii Sergeevich Vladimirov, Tr. Mat. Inst. Steklova, 306, Steklov Math. Inst. RAS, Moscow, 2019 (to appear)  mathnet

   2018
2. N. G. Marchuk, Uravneniya teorii polya i algebry Klifforda, Izd. 2-e, rassh. i dop., LENAND, M., 2018 , 344 pp. http://urss.ru/cgi-bin/db.pl?lang=Ru&blang=ru&page=Book&id=226125
3. N. G. Marchuk, “Classification of extended Clifford algebras”, Russian Math. (Iz. VUZ), 62:11 (2018), 23–27  mathnet  crossref  isi  scopus (cited: 1)

   2016
4. N.G. Marchuk, D.S. Shirokov, “General solutions of one class of field equations”, Rep. Math. Phys., 78:3 (2016), 305–326 , arXiv: 1406.6665  mathnet  crossref  isi (cited: 10)  scopus (cited: 9)
5. N. G. Marchuk, D. S. Shirokov, “Constant solutions of Yang-Mills equations and generalized Proca equations”, J. Geom. Symmetry Phys., 42 (2016), 53–72 , arXiv: 1611.03070  mathnet  crossref  isi (cited: 4)  scopus (cited: 4)

   2015
6. N. G. Marchuk, “Demonstration Representation and Tensor Products of Clifford Algebras”, Proc. Steklov Inst. Math., 290 (2015), 143–154  mathnet  crossref  crossref  isi (cited: 2)  elib  elib  scopus (cited: 2)
7. N. G. Marchuk, “Yadernyi reaktor s zhidkometallicheskim teplonositelem dlya podvodnykh lodok”, O rabotakh G. I. Marchuka po raschetam yadernykh reaktorov, Nash Marchuk, Kniga “Nash Marchuk” - eto dan pamyati Guriyu Ivanovichu, iskrenne vyrazhennaya ego kollegami, uchenikami i blizkimi., ISBN 978-5-7692-1444-8, eds. V.P.Ilin, A.K.Lavrova, A.G.Marchuk, N.A.Pritvits, Ya.I.Fet., Izd-vo SO RAN, Novosibirsk, 2015, 183-187 http://sibran.ru/catalog/FM/165098/
8. N. G. Marchuk, “O moem ottse”, Nash Marchuk, Kniga “Nash Marchuk” – eto dan pamyati Guriyu Ivanovichu, iskrenne vyrazhennaya ego kollegami, uchenikami i blizkimi, ISBN 978-5-7692-1444-8, eds. V. P. Ilin, A. K. Lavrova, A. G. Marchuk, N. A. Pritvits, Ya. I. Fet, Izd-vo SO RAN, Novosibirsk, 2015, 176-182 , 428 pp. http://sibran.ru/catalog/FM/165098/

   2014
9. N. Marchuk, “Nonlinear generalization of the Dirac equation”, Theoretical Physics and its Applications, Selected contributions at the 3rd International Conference on Theoretical Physics (Moscow, June 24–28, 2013), eds. T. F. Kamalov, MIPT, M., 2014, 180–182 , arXiv: 1307.6452
10. N. G. Marchuk, “On a field equation generating a new class of particular solutions to the Yang–Mills equations”, Proc. Steklov Inst. Math., 285 (2014), 197–210  mathnet  crossref  crossref  isi (cited: 1)  elib  elib  scopus (cited: 1)

   2013
11. N. Marchuk, “Tensor products of Clifford algebras”, Dokl. Math., 87:2 (2013), 185–188  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus

   2012
12. N. Marchuk, Field theory equations, Amazon, CreateSpace, 2012 , 290 pp.
13. N. G. Marchuk, D. S. Shirokov, Vvedenie v teoriyu algebr Klifforda, Fazis, Moskva, 2012 , 590 pp.
14. N. Marchuk, “Generalized exterior algebras”, Ukr. J. Phys., 57:4 (2012), 422–425 , arXiv: 1103.5313  mathnet  elib  scopus

   2011
15. N. G. Marchuk, “Dirac–Yang–Mills model equations with a spinor gauge symmetry”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(22) (2011), 118–123  mathnet  crossref  rsci  elib
16. N. Marchuk, “Parametrisations of elements of spinor and orthogonal groups using exterior exponents”, Adv. Appl. Clifford Algebr., 21:3 (2011), 583–590 , arXiv: 0912.5349  crossref  mathscinet  zmath  isi  elib  scopus (cited: 1)
17. N. G. Marchuk, “Exterior polymetric algebras”, Dokl. Math., 83:3 (2011), 400–403  crossref  mathscinet  isi  elib  elib  scopus
18. N. G. Marchuk, “Field theory equations with spinor gauge symmetry”, Dokl. Math., 83:2 (2011), 155–157  crossref  mathscinet  isi  elib  elib  scopus
19. N. Marchuk, “Representations of spinor groups using Grassmann exterior algebra”, From Past to Future: Graßmann's Work in Context, Graßmann Bicentennial Conference (Univ. Potsdam, Potsdam, Germany, September 16–19, 2009), eds. H. J. Petsche, A. C. Lewis, J. Liesen, S. Russ, Birkhäuser, Basel, 2011, 303–309  crossref  isi

   2010
20. N. Marchuk, R. Dyabirov, “A symplectic subgroup of a pseudounitary group as a subset of Clifford algebra”, Adv. Appl. Clifford Algebr., 20:2 (2010), 343–350  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 2)  scopus (cited: 3)
21. N. Marchuk, “Mass generation mechanism for spin-(1/2) fermions in Dirac-Yang-Mills model equations with a symplectic gauge symmetry”, Nuovo Cimento Soc. Ital. Fis. B, 125:10 (2010), 1249–1256  crossref  mathscinet  isi (cited: 2)  elib (cited: 1)  scopus (cited: 2)
22. N. G. Marchuk, “A semipolynomial parameterization of fourth-order spinor groups”, Dokl. Math., 82:1 (2010), 543–545  crossref  isi  elib  elib  scopus

   2009
23. N. G. Marchuk, “A tensor Dirac equation in curved space”, Foundations of probability and physics—5, AIP Conf. Proc., 1101, Amer. Inst. Phys., 2009, 328–338  crossref  mathscinet  zmath  adsnasa  isi  scopus
24. N. G. Marchuk, Uravneniya teorii polya i algebry Klifforda, RKhD, Izhevsk, 2009 , 304 pp.

   2008
25. N. G. Marchuk , D. S. Shirokov, “Unitary spaces on Clifford algebras”, Adv. Appl. Clifford Algebr., 18:2 (2008), 237–254  crossref  mathscinet  zmath  isi (cited: 27)  elib (cited: 21)  scopus (cited: 26)
26. N. G. Marchuk, “Modelnye uravneniya Diraka–Maksvela s psevdounitarnoi simmetriei”, Mezhdunarodnaya konferentsiya po matematicheskoi fizike i ee prilozheniyam, Tezisy dokladov (Samara, 8–13 sentyabrya 2008 g.), 2008, 128
27. N. G. Marchuk, “Nekotorye sledstviya modelnoi sistemy uravnenii Diraka–Maksvella”, Vtoroe rossiisko-armyanskoe soveschanie po matematicheskoi fizike, kompleksnomu analizu i smezhnym voprosam, Tezisy dokladov (Moskva, MIAN, 5–11 oktyabrya 2008 g.), 2008, 45
28. N. G. Marchuk, “Model Dirac–Maxwell equations with pseudounitary symmetry”, Theoret. and Math. Phys., 157:3 (2008), 1723–1732  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 2)
29. N. G. Marchuk, Yu. A. Tsimbalov, “Normalnye matrichnye predstavleniya algebr Klifforda”, Vestnik SamGU - Estestvennonauchnaya seriya, 8:1(67) (2008)

   2006
30. N. G. Marchuk, “New representation of Dirac–Yang–Mills equations”, Russ. J. Math. Phys., 13:4 (2006), 397–413  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 2)  scopus (cited: 2)
31. N. G. Marchuk, “Technique of tensors with values in the Atiyah-Kähler algebra in the new representation of Dirac–Yang–Mills equations”, Russ. J. Math. Phys., 13:3 (2006), 299–314  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 3)  scopus (cited: 3)

   2003
32. N. G. Marchuk, “A coordinate-free form of the Dirac equation for the electron”, Dokl. Math., 68:2 (2003), 281–284  mathnet  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)

   2002
33. N. G. Marchuk, “A concept of Dirac-type tensor equations”, Nuovo Cimento Soc. Ital. Fis. B (12), 117:12 (2002), 1357–1385  mathscinet  isi (cited: 5)  elib (cited: 5)  scopus (cited: 5)
34. N. G. Marchuk, “Dirac-type tensor equations on a parallelisable manifold”, Nuovo Cimento Soc. Ital. Fis. B (12), 117:7 (2002), 789–796  mathscinet  isi (cited: 2)  elib (cited: 2)  scopus (cited: 2)
35. N. G. Marchuk, “The Dirac equation vs. the Dirac-type tensor equation”, Nuovo Cimento Soc. Ital. Fis. B (12), 117:5 (2002), 511–520  mathscinet  isi (cited: 5)  elib (cited: 8)  scopus (cited: 6)
36. N. G. Marchuk, “Dirac-type tensor equations with non-abelian gauge symmetries on pseudo-Riemannian space”, Nuovo Cimento Soc. Ital. Fis. B (12), 117:1 (2002), 95–119  mathscinet  adsnasa  isi (cited: 8)  elib (cited: 9)  scopus (cited: 8)
37. N. G. Marchuk, “Addendum to the paper: Dirac-type tensor equations with non-abelian gauge symmetries on pseudo-Riemannian space”, Nuovo Cimento Soc. Ital. Fis. B (12), 117:5 (2002), 613–614  mathscinet  adsnasa  isi (cited: 4)  scopus (cited: 3)

   2001
38. N. G. Marchuk, “Dirac-type tensor equations”, Nuovo Cimento Soc. Ital. Fis. B (12), 116:11 (2001), 1225–1248  mathscinet  isi (cited: 9)  elib (cited: 11)  scopus (cited: 11)
39. N. Marchuk, “The Dirac type tensor equation in Riemannian space”, Clifford analysis and its applications (Prague, 2000), NATO Sci. Ser. II Math. Phys. Chem., 25, Kluwer Acad. Publ., Dordrecht, 2001, 223–230  mathscinet  zmath  isi

   2000
40. N. G. Marchuk, “Dirac equation in Riemannian space without tetrads”, Nuovo Cimento Soc. Ital. Fis. B (12), 115:11 (2000), 1267–1301  mathscinet  isi (cited: 7)  elib (cited: 7)  scopus (cited: 9)
41. N. G. Marchuk, Model equation for a description of local interaction of a fermion with electromagnetic and gravitational fields, Preprint UTMS 2000-15, February 21, 2000, University of Tokyo, University of Tokyo, Graduate School of Mathematical Sciences, Komaba, Tokyo, Japan, 2000 , 47 pp.

   1998
42. N. G. Marchuk, “Gauge fields of the matrix Dirac equation”, Nuovo Cimento Soc. Ital. Fis. B (12), 113:10 (1998), 1287–1295  mathscinet  adsnasa  isi (cited: 2)  elib (cited: 4)  scopus (cited: 3)
43. N. G. Marchuk, “Dirac $\gamma$-equation, classical gauge fields and Clifford algebra”, Adv. Appl. Clifford Algebras, 8:1 (1998), 181–225  crossref  mathscinet  zmath

   1997
44. N. G. Marchuk, “The matrix Dirac equation”, Dokl. Math., 55:3 (1997), 453–455  mathnet  mathscinet  zmath  isi  elib (cited: 1)  scopus (cited: 1)

   1995
45. N. G. Marchuk, “A model of compound structure of quarks, leptons, and the quanta of interaction between them”, Dokl. Math., 52:2 (1995), 275–277  zmath  isi

   1994
46. N. Marchuk, A new representation of the Dirac equation using even and odd gamma-matrices, Preprint CTS of IISc/94/1, Indian Institute of Science, Centre for High Energy Physics, Bangalore, India, 1994 , 7 pp.

   1993
47. N. Marchuk, New form of Dirac equation, IMSc/93/7, The Institute of Mathematical Sciences (IMSc), Madras, India, 1993 , 6 pp.

   1992
48. A. A. Dezin, N. G. Marchuk, “Perturbation of periodicity conditions in the simplest nonlinear model”, Russian Acad. Sci. Dokl. Math., 45:2 (1992), 467–469 (1993)  mathnet  mathscinet  zmath  isi

   1988
49. N. G. Marchuk, “Symmetric hyperbolic systems of second order equations”, Soviet Math. Dokl., 37:1 (1988), 207–212  mathnet  mathscinet  zmath  isi

   1987
50. N. G. Marchuk, “A mixed problem for the vector wave equation”, Sov. Math. Dokl., 35 (1987), 230–232  mathnet  mathscinet  zmath  isi

   1986
51. N. G. Marchuk, “O korrektnosti nachalno-kraevoi zadachi dlya volnovogo uravneniya s granichnym usloviem vtorogo poryadka”, Sib. matem. zhurn., 27:6 (1986), 140–143  mathscinet  zmath  isi
52. N. G. Marchuk, “Giperbolicheski simmetrizuemye sistemy uravnenii”, Differents. uravneniya, 22:4 (1986), 652–662  mathnet  mathscinet  zmath  isi
53. N. G. Marchuk, “Spetsialnyi klass formul Grina”, Differents. uravneniya, 22:2 (1986), 315–326  mathnet  mathscinet  zmath
54. V. V. Zharinov, N. G. Marchuk, “Green's formulas and bilinear conservation laws”, Math. Notes, 40:4 (1986), 776–780  mathnet  crossref  mathscinet  zmath  isi  scopus

   1985
55. N. G. Marchuk, “A large class of Green formulas and conservation laws”, Sov. Math. Dokl., 32 (1985), 892–894  mathnet  mathscinet  zmath  isi

   1984
56. N. G. Marchuk, “On a method of reducing the wave equation to a system of first order equations”, Sov. Math. Dokl., 29 (1984), 685–687  mathnet  mathscinet  zmath  isi
57. N. G. Marchuk, “O korrektnosti postanovki smeshannoi zadachi dlya vektornogo volnovogo uravneniya”, Differents. uravneniya, 20:5 (1984), 838–843  mathnet  mathscinet  zmath  isi
58. N. G. Marchuk, “Svedenie zadachi Koshi dlya volnovogo uravneniya k zadache Koshi dlya sistemy uravnenii pervogo poryadka”, Differents. uravneniya, 20:4 (1984), 653–659  mathnet  mathscinet  zmath  isi

   1982
59. N. G. Marchuk, “Suschestvovanie resheniya smeshannoi zadachi dlya vektornogo giperbolicheskogo uravneniya vtorogo poryadka”, Sib. matem. zhurn., 23:1 (1982), 70–84  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)

   1980
60. N. G. Marchuk, “On the existence of solutions of a mixed problem for the vector wave equation”, Sov. Math. Dokl., 21 (1980), 785–788  mathnet  mathscinet  mathscinet  zmath  isi

   1979
61. N. Marchuk, Issledovanie korrektnosti linearizovannoi teorii udarnoi volny s pomoschyu integralov energii, Preprint VTs SO AN, № 153, Vychislitelnyi Tsentr Sibirskogo Otdeleniya AN, Novosibirsk, 1979 , 33 pp.

Presentations in Math-Net.Ru
1. Generalized Clifford algebras
Nikolay Marchuk
New Trends in Mathematical and Theoretical Physics
October 7, 2016 15:00   
2. Развитие концепции модельных уравнений поля
N. G. Marchuk
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
November 5, 2015 11:00
3. Новый класс решений уравнений Янга–Миллса
N. G. Marchuk
Conference "Mathematical Physics. Vladimirov-90" dedicated to the 90th anniversary of academician V. S. Vladimirov
November 13, 2013 15:30   
4. Новый класс решений уравнений Янга–Миллса
N. G. Marchuk
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
October 17, 2013 11:00
5. Некоторые уравнения дираковского типа
N. G. Marchuk
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
October 20, 2005
6. Техника тензоров со значениями в алгебре Атьи–Келера и представлении группы $\mathrm{Spin}(1,3)$
N. G. Marchuk
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
November 4, 2004
7. Dirac-type tensor equations
N. G. Marchuk
Steklov Mathematical Institute Seminar
June 17, 2004 16:00   
8. Тензорные уравнения дираковского типа
N. G. Marchuk
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
June 3, 2004

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