Persons: Marchuk, Nikolay Gur'evich

Persons

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

Marchuk, Nikolay Gur'evich

Statistics
in MathSciNet:	47 (47)
in zbMATH:	32 (32)
in Web of Science:	51 (51)
in Scopus:	36 (36)

Doctor of physico-mathematical sciences

Speciality:

01.01.03 (Mathematical physics)

Birth date:

16.10.1955

E-mail:

Website:

https://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:

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

https://www.mathnet.ru/eng/person18563

List of publications on Google Scholar

https://zbmath.org/authors/ai:marchuk.nikolaj-gurevich

https://mathscinet.ams.org/mathscinet/MRAuthorID/203675

https://elibrary.ru/author_items.asp?authorid=14076

https://www.webofscience.com/wos/author/record/J-6168-2013

https://www.scopus.com/authid/detail.url?authorId=6602450293

List of scientific publications:

scientific publications

		Citations (Crossref Cited-By Service + Math-Net.Ru)


2025
1.	N. G. Marchuk, Eskiz kalibrovochnoi modeli gravitatsii s SU(2) simmetriei na lorentsevom mnogoobrazii s tetradoi, 2025 , 30 pp., arXiv: 2501.13112
2.	“Nauchnye interesy Guriya Ivanovicha Marchuka - kakie i pochemu”, Glava 27: N. G. Marchuk, Aktualnye problemy vychislitelnoi matematiki i matematicheskogo modelirovaniya (k 100-letiyu Guriya Ivanovicha Marchuka), Kollektivnaya monografiya, podgotovlennaya kollegami, uchenikami i vnuchatymi uchenikami akademika Guriya Ivanovicha Marchuka k 100-letiyu so dnya rozhdeniya, eds. V. P. Dymnikov, E. E. Tyrtyshnikov, V. P. Ilin, SO RAN, Novosibirsk, 2025, 648–665 , IVM IMG SO RAN, 2025
3.	N. G. Marchuk, “Conservative equations in field theory: conservation and symmetry laws”, Differ. Equ., 61:6 (2025), 872–892
4.	N. G. Marchuk, “Classification of field equations for Weyl and Elko spinors”, Differ. Equ., 61:3 (2025), 388–345

2024
5.	N. G. Marchuk, “A class of field equations for neutrinos with nonzero masses”, Theoret. and Math. Phys., 219:3 (2024), 897–912
6.	N. G. Marchuk, V. P. Ilin, “Gurii Ivanovich Marchuk (1925–2013)”, Statya o nauchnykh interesakh i zhiznennom puti poslednego prezidenta AN SSSR (s 1986 po 1991) Marchuka G.I., Rossiiskaya akademiya nauk: 300 let istorii, v 2-kh tomakh, v. 2, Akademiya nauk SSSR-Rossiiskaya akademiya nauk. 1934-2024, Nauka, M., 2024, 735–752 {https://www.cnb.dvo.ru/2024/09/20/novye-postupleniya/novye-postupleniya-v-biblioteku-2024-god/rossijskaya-akademiya-nauk-300-let-istorii-v-dvuh-tomah-tom-2/

2023
7.	N. G. Marchuk, Uravneniya teorii polya i algebry Klifforda, Izd. 2, rassh. i dop., Izdatelskaya gruppa URSS, Moskva, 2023 , 344 pp. https://urss.ru/cgi-bin/db.pl?lang=RU&blang=ru&page=Book&id=302823

2021
8.	N. G. Marchuk, D. S. Shirokov, Teoriya algebr Klifforda i spinorov, Krasand (URSS), Moskva, 2021 , 560 pp. http://urss.ru/cgi-bin/db.pl?lang=Ru&blang=ru&page=Book&id=263794
9.	Nikolay Marchuk, “Sketch of a gauge model of gravity with $SU(2)$ symmetry in Minkowski space”, Adv. Appl. Clifford Algebr., 31 (2021), 75 , 14 pp.

2020
10.	N. G. Marchuk, “Model Dirac and Dirac–Hestenes Equations as Covariantly Equipped Systems of Equations”, Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunovs Legacy, A liber Amicorum to Professor Godunov, eds. Demidenko, G.V., Romenski, E., Toro, E., Dumbser, M. (Eds.), Springer, 2020, 269–276 https://www.springer.com/gp/book/9783030388690 ; arXiv: 1910.08407
11.	Nikolay G. Marchuk, Dmitry S. Shirokov, “Local Generalization of Paulis Theorem”, Azerb. J. Math., 10:1 (2020), 38–56 , arXiv: 1201.4985	2 ^[x]
12.	N. G. Marchuk, D. S. Shirokov, “On some equations modeling the Yang-Mills equations”, Phys. Part. Nucl., 51:4 (2020), 589–594
13.	N. G. Marchuk, “One Class of Relativistically Invariant First-Order Equations”, Differ. Equ., 56:12 (2020), 1575–1586

2019
14.	N. G. Marchuk, “A Generalization of the Yang–Mills Equations”, Proc. Steklov Inst. Math., 306 (2019), 157–177

2018
15.	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
16.	N. G. Marchuk, “Classification of extended Clifford algebras”, Russian Math. (Iz. VUZ), 62:11 (2018), 23–27 , arXiv: 1611.07684

2016
17.	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	13 ^[x]
18.	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	8 ^[x]

2015
19.	N. G. Marchuk, “Demonstration Representation and Tensor Products of Clifford Algebras”, Proc. Steklov Inst. Math., 290 (2015), 143–154
20.	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/
21.	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
22.	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
23.	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

2013
24.	N. Marchuk, “Tensor products of Clifford algebras”, Dokl. Math., 87:2 (2013), 185–188

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

2011
28.	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
29.	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	1 ^[x]
30.	N. G. Marchuk, “Exterior polymetric algebras”, Dokl. Math., 83:3 (2011), 400–403
31.	N. G. Marchuk, “Field theory equations with spinor gauge symmetry”, Dokl. Math., 83:2 (2011), 155–157
32.	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
33.	N .G. Marchuk, Modelnye uravneniya teorii polya s unitarnoi i psevdounitarnoi kalibrovochnoi simmetriei, Diss. doktora fiz.-mat. nauk, Matematicheskii Institut im. V. A. Steklova RAN, Moskva, 2011 , 252 pp.

2010
34.	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 , arXiv: arXiv:0810.3293	2 ^[x]
35.	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 , arXiv: arXiv:1009.3701
36.	N. G. Marchuk, “A semipolynomial parameterization of fourth-order spinor groups”, Dokl. Math., 82:1 (2010), 543–545

2009
37.	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
38.	N. G. Marchuk, Uravneniya teorii polya i algebry Klifforda, RKhD, Izhevsk, 2009 , 304 pp.

2008
39.	N. G. Marchuk , D. S. Shirokov, “Unitary spaces on Clifford algebras”, Adv. Appl. Clifford Algebr., 18:2 (2008), 237–254 , arXiv: arXiv:0705.1641	32 ^[x]
40.	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
41.	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
42.	N. G. Marchuk, “Model Dirac–Maxwell equations with pseudounitary symmetry”, Theoret. and Math. Phys., 157:3 (2008), 1723–1732
43.	N. G. Marchuk, Yu. A. Tsimbalov, “Normalnye matrichnye predstavleniya algebr Klifforda”, Vestnik SamGU - Estestvennonauchnaya seriya, 8:1(67) (2008)

2006
44.	N. G. Marchuk, “New representation of Dirac–Yang–Mills equations”, Russ. J. Math. Phys., 13:4 (2006), 397–413	2 ^[x]
45.	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	3 ^[x]

2003
46.	N. G. Marchuk, “A coordinate-free form of the Dirac equation for the electron”, Dokl. Math., 68:2 (2003), 281–284 , arXiv: arXiv:math-ph/0307042
47.	N. G. Marchuk, S. E. Martynova, Notions of determinant, spectrum, and Hermitian conjugation of Clifford algebra elements, 2003 , 7 pp., arXiv: math-ph/0307043
48.	N. G. Marchuk, A model of composite structure of quarks and leptons, 2003 , 7 pp., arXiv: hep-ph/0211459

2002
49.	N. G. Marchuk, “A concept of Dirac-type tensor equations”, Nuovo Cimento Soc. Ital. Fis. B (12), 117:12 (2002), 1357–1385 , arXiv: arXiv:math-ph/0212006
50.	N. G. Marchuk, “Dirac-type tensor equations on a parallelisable manifold”, Nuovo Cimento Soc. Ital. Fis. B (12), 117:7 (2002), 789–796 , arXiv: arXiv:math-ph/0211072
51.	N. G. Marchuk, “The Dirac equation vs. the Dirac-type tensor equation”, Nuovo Cimento Soc. Ital. Fis. B (12), 117:5 (2002), 511–520 , arXiv: arXiv:math-ph/0211073
52.	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 , arXiv: arXiv:math-ph/0205022
53.	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 , arXiv: arXiv:math-ph/0211074

2001
54.	N. G. Marchuk, “Dirac-type tensor equations”, Nuovo Cimento Soc. Ital. Fis. B (12), 116:11 (2001), 1225–1248 , arXiv: arXiv:math-ph/0007025
55.	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

2000
56.	N. G. Marchuk, “Dirac equation in Riemannian space without tetrads”, Nuovo Cimento Soc. Ital. Fis. B (12), 115:11 (2000), 1267–1301 , arXiv: arXiv:math-ph/0010045
57.	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. arXiv:math-ph/9912004

1998
58.	N. G. Marchuk, “Gauge fields of the matrix Dirac equation”, Nuovo Cimento Soc. Ital. Fis. B (12), 113:10 (1998), 1287–1295 , arXiv: arXiv:math-ph/9811021
59.	N. G. Marchuk, “Dirac $\gamma$-equation, classical gauge fields and Clifford algebra”, Adv. Appl. Clifford Algebras, 8:1 (1998), 181–225 , arXiv: arXiv:math-ph/9811022	10 ^[x]
60.	N. G. Marchuk, A model of the composite structure of quarks and leptons with SU(4) gauge symmetry, 1998 , 8 pp., arXiv: hep-ph/9801382

1997
61.	N. G. Marchuk, “The matrix Dirac equation”, Dokl. Math., 55:3 (1997), 453–455

1995
62.	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

1994
63.	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
64.	N. Marchuk, New form of Dirac equation, IMSc/93/7, The Institute of Mathematical Sciences (IMSc), Madras, India, 1993 , 6 pp.

1992
65.	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)

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

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

1986
68.	N. G. Marchuk, “The well-posedness of an initial-boundary value problem for the wave equation with a second-order boundary condition”, Siberian Math. J., 27:6 (1986), 900–903
69.	N. G. Marchuk, “Giperbolicheski simmetrizuemye sistemy uravnenii”, Differents. uravneniya, 22:4 (1986), 652–662
70.	N. G. Marchuk, “Spetsialnyi klass formul Grina”, Differents. uravneniya, 22:2 (1986), 315–326
71.	V. V. Zharinov, N. G. Marchuk, “Green's formulas and bilinear conservation laws”, Math. Notes, 40:4 (1986), 776–780

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

1984
73.	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
74.	N. G. Marchuk, “O korrektnosti postanovki smeshannoi zadachi dlya vektornogo volnovogo uravneniya”, Differents. uravneniya, 20:5 (1984), 838–843
75.	N. G. Marchuk, “Svedenie zadachi Koshi dlya volnovogo uravneniya k zadache Koshi dlya sistemy uravnenii pervogo poryadka”, Differents. uravneniya, 20:4 (1984), 653–659

1982
76.	N. G. Marchuk, “Existence of a solution of a mixed problem for a second-order vector hyperbolic equation”, Siberian Math. J., 23:1 (1982), 53–64

1980
77.	N. G. Marchuk, “On the existence of solutions of a mixed problem for the vector wave equation”, Sov. Math. Dokl., 21 (1980), 785–788
78.	N .G. Marchuk, O suschestvovanii reshenya smeshannoi zadachi dlya vektornogo volnovogo uravneniya, Preprint № 216, Vychislitelnyi Tsentr SOAN SSSR, Novosibirsk, 1980 , 22 pp.
79.	N .G. Marchuk, Suschestvovanie reshenii smeshannoi zadachi dlya volnovogo uravneniya s granichnym usloviem vtorogo poryadka, Preprint № 239, Vychislitelnyi Tsentr SOAN SSSR, Novosibirsk, 1980 , 10 pp.
80.	N .G. Marchuk, Suschestvovanie reshenii smeshannoi zadachi dlya vektornogo volnovogo uravneniya, Diss. kand. fiz.-mat. nauk, Institut Gornogo dela SOAN SSSR, Novosibirsk, 1980 , 74 pp.

1979
81.	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.

1978
82.	N .G. Marchuk, Integral energii v smeshannoi zadache dlya giperbolicheskogo uravneniya, Preprint № 109, Vychislitelnyi Tsentr SOAN SSSR, Novosibirsk, 1978 , 17 pp.

Presentations in Math-Net.Ru

1.	Уравнение Ланцоша (1929) как альтернатива уравнению Дирака (1928) N. G. Marchuk Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS November 27, 2025 11:00
2.	О некоторых результатах Г.И. Марчука, связанных с ядерной энергией N. G. Marchuk The Sixth International Conference "Supercomputer Technologies of Mathematical Modelling" (SCTeMM'25) July 16, 2025 16:00
3.	Уравнение для нейтрино с ненулевой массой N. G. Marchuk International scientific conference “Infinite-dimensional analysis and mathematical physics” (IDAMPh 2025) January 27, 2025 16:00
4.	Some relativistic invariant systems of differential equations N. G. Marchuk International Conference Dedicated to the 100th Anniversary of the Birthday of V. S. Vladimirov (Vladimirov-100) January 11, 2023 16:30
5.	Об одном модельном уравнении теории поля N. G. Marchuk Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS November 25, 2021 11:00
6.	One class of relativistic invariant systems of equations of first order N. G. Marchuk International Conference "Selected Topics in Mathematical Physics" Dedicated to 75-th Anniversary of I. V. Volovich September 30, 2021 14:00
7.	Model Dirac and Dirac–Hestenes equations as covariantly equipped system of equations N. G. Marchuk Mathematical Physics, Dynamical Systems and Infinite-Dimensional Analysis – 2021 July 9, 2021 12:15
8.	Обобщение уравнений Янга-Миллса N. G. Marchuk Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS April 22, 2020 11:00
9.	Generalized Clifford algebras Nikolay Marchuk New Trends in Mathematical and Theoretical Physics October 7, 2016 15:00
10.	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
11.	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
12.	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
13.	Некоторые уравнения дираковского типа N. G. Marchuk Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS October 20, 2005
14.	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
15.	Dirac-type tensor equations N. G. Marchuk Steklov Mathematical Institute Seminar June 17, 2004 16:00
16.	Тензорные уравнения дираковского типа N. G. Marchuk Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS June 3, 2004

Organisations