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[[:Kategori:Slavere]]
[[:Kategori:Ukrainere]]
Nikolay Bogolyubov was born on 21 August 1909 in [[Nizhny Novgorod]], [[Russian Empire]] to [[Russian Orthodox Church]] [[priest]] and [[seminary]] teacher of [[theology]], [[psychology]] and [[philosophy]] Nikolay Mikhaylovich Bogolyubov, and Olga Nikolayevna Bogolyubova, a teacher of music.
The Bogolyubovs relocated to the village of Velikaya Krucha in the [[Poltava Governorate]] (now in [[Poltava Oblast]], [[Ukraine]]) in 1919, where the young Nikolay Bogolyubov began to study physics and mathematics. The family soon moved to [[Kiev]] in 1921, where they continued to live in poverty as the elder Nikolay Bogolyubov only found a position as a priest in 1923.<ref name = "A.N. Bogolyubov 2009">Bogolyubov, A. N. (2009). ''[http://bogolubov.jinr.ru/biography.php "Nikolay Nikolayevich Bogolyubov".]'' ''N. N. Bogolyubov: K 100-letiyu so dnya rozhdeniya'' (Joint Institute for Nuclear Research). Retrieved 8 January 2012. {{ru icon}}</ref>
He attended research seminars in [[Kiev University]] and soon started to work under the supervision of the well-known contemporary mathematician [[Nikolay Mitrofanovich Krylov|Nikolay Krylov]]. In 1924, at the age of 15, Nikolay Bogolyubov wrote his first published scientific paper ''On the behavior of solutions of linear differential equations at infinity''. In 1925 he entered Ph.D. program at the Academy of Sciences of the [[Ukrainian SSR]] and obtained the degree of [[Kandidat Nauk]] (''Candidate of Sciences'', equivalent to a Ph.D.) in 1928, at the age of 19, with the doctoral thesis titled ''On direct methods of variational calculus''. In 1930, at the age of 21, he obtained the degree of [[Doktor nauk]] (''Doctor of Sciences'', equivalent to [[Habilitation]]), the highest degree in the Soviet Union, which requires the recipient to have made a significant independent contribution to his or her scientific field.
This early period of Bogolyubov's work in science was concerned with such mathematical problems as direct methods of the [[calculus of variations]], the theory of [[almost periodic function]]s, methods of approximate solution of [[differential equation]]s, and [[dynamical systems]]. This earlier research had already earned him recognition. One of his essays was awarded the [[Bologna Academy of Sciences]] Prize in 1930, and the author was awarded the erudite degree of doctor of mathematics. This was the period when the scientific career of the young Nikolai Bogolyubov began, later producing new scientific trends in modern mathematics, physics, and mechanics.
Since 1931, Krylov and Bogolyubov worked together on the problems of nonlinear mechanics and nonlinear oscillations. They were the key figures in the "Kiev school of nonlinear oscillation research", where their cooperation resulted in the paper "''On the quasiperiodic solutions of the equations of nonlinear mechanics''" (1934) and the book ''Introduction to Nonlinear Mechanics'' (1937; translated to English in 1947) leading to a creation of a large field of non-linear mechanics.
{{Quotation|And this can explain, as the authors believe, the need to shape the collection of problems of non-linear perturbation theory into a special science, which could be named NON-LINEAR MECHANICS.|N. M. Krylov and N. N. Bogolyubov|New methods in non-linear mechanics|ONTI GTTI, Moscow-Leningrad, 1934}}
Distinctive features of the Kiev School approach included an emphasis on the computation of solutions (not just a proof of its existence), approximations of periodic solutions, use of the invariant manifolds in the phase space, and applications of a single unified approach to many different problems. From a [[control engineering]] point of view, the key achievement of the Kiev School was the development by Krylov and Bogolyubov of the [[describing function]] method for the analysis of nonlinear control problems.
In the period 1928—1973, Nikolay Bogolyubov worked in the [http://www.bitp.kiev.ua/index.php?lang=en Institute for Theoretical Physics] of the Academy of Sciences of the Ukrainian SSR holding the position of the Director of the institute since 1965. He lectured at Kiev University in the period 1936—1959.
===In evacuation (1941–1943)===
After the [[Operation Barbarossa|German attack]] against the [[Soviet Union]] on 22 June 1941 (beginning of the [[Great Patriotic War (term)|Great Patriotic War]]), most institutes and universities from west part of Russia were evacuated into east regions far from the battle lines. Nikolay Bogolyubov moved to [[Ufa]], where he became Head of the Departments of Mathematical Analysis at [[Ufa State Aviation Technical University]] and at [[Bashkir State University|Ufa Pedagogical Institute]], remaining on these positions during the period of July 1941 – August 1943.
===Moscow (1943–?)===
In autumn 1943, Bogolyubov came from evacuation to Moscow and on 1 November 1943 he accepted a position in the Department of Theoretical Physics at the [[Moscow State University]] (MSU). At that time the Head of the Department was [[Anatoly Vlasov]] (for a short period in 1944 the Head of the Department was [[Vladimir Fock]]). Theoretical physicists working in the department in that period included [[Dmitry Ivanenko]], [[Arsenij Sokolov]], and other physicists.
In the period 1943–1946, Bogolyubov's resesarch was essentially concerned with the theory of [[stochastic process]]es and asymptotic methods. In his work {{citation needed|date=March 2014}} a simple example of an [[anharmonic oscillator]] evolving under the force of the form as a superposition of incoherent sinusoidal oscillations with continuous spectrum was used to show that depending on a specific approximation time scale the evolution of the system can be either deterministic, or a stochastic process satisfying [[Fokker-Planck equation]], or even a process which is neither deterministic nor stochastic. In other words, he showed that depending on the choice of the time scale for the corresponding approximations the same stochastic process can be regarded as both dynamical and [[Markov process|Markovian]], and in the general case as a non-Markov process. This work was the first to introduce the notion of time hierarchy in non-equilibrium statistical physics which then became the key concept in all further development of the statistical theory of irreversible processes.
In 1945, Bogolyubov proved a fundamental theorem on the existence and basic properties of a one-parameter integral manifold for a system of non-linear differential equations. He investigated periodic and quasi-periodic solutions lying on a one-dimensional manifold, thus forming the foundation for a new method of non-linear mechanics, the ''method of integral manifolds''.
In 1946, he published in [[JETP]] two works on equilibrium and non-equilibrium statistical mechanics which became the essence of his fundamental monograph ''Problems of dynamical theory in statistical physics'' (Moscow, 1946).
On 26 January 1953, Nikolay Bogolyubov became the Head of the Department of Theoretical Physics at MSU, after Anatoly Vlasov decided to leave the position on January 2, 1953.
===Steklov Institute (1947–?)===
[[File:N.Bogolyubov.jpg|thumb|N.Bogolyubov]]
In 1947, Nikolay Bogolyubov organized and became the Head of the Department of Theoretical Physics at the [[Steklov Mathematical Institute]]. In 1969, the Department of Theoretical Physics was separated into the Departments of Mathematical Physics (Head [[Vasily Vladimirov]]), of Statistical Mechanics, and of Quantum Field Theory (Head [[Mikhail Polivanov]]). While working in the Steklov Institute, Nikolay Bogolyubov and his school contributed to science with many important works including works on renormalization theory, [[renormalization group]], axiomatic [[S-matrix]] theory, and works on the theory of dispersion relations.
In the late 1940s and 1950s, Bogoliubov worked on the theory of [[superfluid]]ity and [[superconductivity]], where he developed the method of [[BBGKY hierarchy]] for a derivation of kinetic equations, formulated microscopic theory of superfluidity, and made other essential contributions. Later he worked on [[quantum field theory]], where introduced the [[Bogoliubov transformation]], formulated and proved the [[edge-of-the-wedge theorem|Bogoliubov's edge-of-the-wedge theorem]] and [[Bogoliubov-Parasyuk theorem]] (with [[Ostap Parasyuk]]), and obtained other significant results. In the 1960s his attention turned to the [[quark]] model of [[hadrons]]; in 1965 he was among the first scientists to study the new [[quantum number]] [[color charge]].
In 1946, Nikolay Bogoliubow was elected as a Corresponding Member of the [[Academy of Sciences of the USSR]]. He was elected a full member ([[academician]]) of the Academy of Sciences of the Ukrainian SSR and in full member of the Academy of Sciences of the USSR in 1953.
;Soviet
* Two [[Stalin Prize]]s (1947, 1953)
* [[Order of the Red Banner of Labour]], twice (1948, 1954)
* [[Order of the Badge of Honour]], twice (1944, 1944)
;Memory
Institutions, awards and locations have been named in Bogolyubov's memory:
* Bogoliubov Institute of Theoretical Physics [[National Academy of Sciences of Ukraine]] (Kiev, Ukraine)
* [[Bogolyubov Prize (NASU)|Bogolyubov Prize]] ([[National Academy of Sciences of Ukraine]]) for scientists with outstanding contribution to theoretical physics and applied mathematics
* Commemorative plaque at the entrance of the Physics Department of Moscow State University
In 2009, the [[centenary]] of Nikolay Bogolyubov's birth was celebrated with two conferences in Russia and Ukraine:
*[http://theor.jinr.ru/~bog2009/ International Bogolyubov Conference: Problems of Theoretical and Mathematical Physics] 21–27 August, Moscow-Dubna, Russia.
*[http://www.bitp.kiev.ua/bogolyubov2009/ Bogolyubov Kyiv Conference: Modern Problems of Theoretical and Mathematical Physics] 15–18 September, [[Kiev]], Ukraine.
==Research==
Fundamental works of Nikolay Bogoliubov were devoted to asymptotic methods of nonlinear mechanics, quantum field theory, statistical field theory, variational calculus, approximation methods in mathematical analysis, equations of mathematical physics, theory of stability, theory of dynamical systems, and to many other areas.
He built a new theory of scattering matrices, formulated the concept of [[Bogoliubov causality condition|microscopical causality]], obtained important results in quantum electrodynamics, and investigated on the basis of the [[edge-of-the-wedge theorem]] the dispersion relations in elementary particle physics. He suggested a new synthesis of the Bohr theory of quasiperiodic functions and developed methods for asymptotic integration of nonlinear differential equations which describe oscillating processes.
===Mathematics and non-linear mechanics===
*In 1932—1943, in the early stage of his career, he worked in collaboration with [[Nikolay Mitrofanovich Krylov|Nikolay Krylov]] on mathematical problems of nonlinear mechanics and developed mathematical methods for asymptotic integration of non-linear differential equations. He also applied these methods to problems of statistical mechanics.
*In 1937, jointly with Nikolay Krylov he proved the [[Krylov-Bogoliubov theorem]]s.<ref>{{Cite journal|doi=10.2307/1968511|author=N. N. Bogoliubov and N. M. Krylov|journal=Annals of Mathematics | series = Second Series|volume=38|issue=1|pages=65–113|year=1937|jstor=1968511|title=La theorie generalie de la mesure dans son application a l'etude de systemes dynamiques de la mecanique non-lineaire|language=French}} Zbl. 16.86.</ref>
*In 1956, at the International Conference on Theoretical Physics in Seattle, USA (September, 1956), he presented the formulation and the first proof of the [[Bogoliubov's edge-of-the-wedge theorem|edge-of-the-wedge theorem]]. This theorem in the theory of functions of several complex variables has important implications to the dispersion relations in elementary particle physics.
===Statistical mechanics===
*1939 Jointly with [[Nikolay Mitrofanovich Krylov|Nikolay Krylov]] gave the first consistent microscopic derivation of the [[Fokker-Planck equation]] in the single scheme of classical and quantum mechanics.<ref>N. N. Bogoliubov and [[Nikolay Mitrofanovich Krylov|N. M. Krylov]] (1939). ''Fokker-Planck equations generated in perturbation theory by a method based on the spectral properties of a perturbed Hamiltonian''. Zapiski Kafedry Fiziki Akademii Nauk Ukrainian SSR '''4''': 81–157 (in Ukrainian).</ref>
*1945 Suggested the idea of hierarchy of [[relaxation time]]s, which is significant for statistical theory of [[irreversible process]]es.
*1946 Developed a general method for a microscopic derivation of kinetic equations for classical systems.<ref>{{Cite journal|author=N. N. Bogoliubov|title=Kinetic Equations|journal=[[JETP|Journal of Experimental and Theoretical Physics]]|volume=16|pages=691–702|year=1946|url=|language=Russian|issue=8}}</ref><ref>{{Cite journal|author=N. N. Bogoliubov|title=Kinetic Equations|journal=Journal of Physics|volume=10|pages=265–274|year=1946|url=|issue=3}}</ref> The method was based on the hierarchy of equations for multi-particle distribution functions known now as [[BBGKY hierarchy|Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy]].
*1947 Jointly with [[Kirill Gurov|K. P. Gurov]] extended this method to the derivation of kinetic equations for quantum systems on the basis of the quantum BBGKY hierarchy.<ref>{{Cite journal|author=N. N. Bogoliubov, K. P. Gurov|title=Kinetic Equations in Quantum Mechanics|journal=[[JETP|Journal of Experimental and Theoretical Physics]]|volume=17|pages=614–628|year=1947|url=|language=Russian|issue=7}}</ref>
*1947—1948 Introduced kinetic equations in the theory of [[superfluidity]],<ref>{{Cite journal|author=N. N. Bogoliubov|title=On the Theory of Superfluidity|journal=Izv. Academii Nauk USSR|volume=11|pages=77|year=1947|url=|language=Russian|issue= 1}}</ref><ref>{{Cite journal|author=N. N. Bogoliubov|title=On the Theory of Superfluidity|journal=Journal of Physics|volume=11|pages=23–32|year=1947|url=|issue=1}}</ref> computed the excitation spectrum for a weakly imperfect [[Bose gas]], showed that this spectrum has the same properties as spectrum of [[Helium#Helium II state|Helium II]], and used this analogy for a theoretical description of superfluidity of Helium II.
*1958 Formulated a microscopic theory of [[superconductivity]]<ref>{{Cite journal|author=N. N. Bogoliubov|title=On a New Method in the Theory of Superconductivity|journal=[[JETP|Journal of Experimental and Theoretical Physics]]|volume=34 | issue = 1 |pages=58|year=1958|url=}}</ref> and established an analogy between superconductivity and superfluidity phenomena; this contribution was discussed in details in the book ''A New Method in the Theory of Superconductivity'' (co-authors V. V. Tolmachev and [[Dmitry Shirkov|D. V. Shirkov]], Moscow, Academy of Sciences Press, 1958).
===Quantum theory===
*1955 Developed an axiomatic theory for [[scattering matrix]] (''S''—matrix) in quantum field theory and introduced the [[Bogoliubov causality condition|causality condition]] for ''S''—matrix in terms of variational derivatives.
*1955 Jointly with [[Dmitry Shirkov]] developed the [[renormalization group]] method.
*1955 Jointly with [[Ostap Parasyuk]] proved the theorem on the finiteness and uniqueness (for renormalizable theories) of the scattering matrix in any order of perturbation theory ([[Bogoliubov-Parasyuk theorem]]) and developed a procedure ([[R-operation]]) for a practical subtraction of singularities in quantum field theory.<ref>{{Cite journal|author=N. N. Bogoliubov, O. S. Parasyuk|title=[A theory of multiplication of causal singular functions]|journal=[[Doklady Akademii Nauk SSSR]]|volume=100|pages=25–28|year=1955|url=|language=Russian}}</ref><ref>{{Cite journal|author=N. N. Bogoliubov, O. S. Parasyuk|title=Uber die Multiplikation der Kausalfunktionen in der Quantentheorie der Felder|journal=Acta Mathematica|volume=97|pages=227–266|year=1957|doi=10.1007/BF02392399|language=German|url=http://www.springerlink.com/content/11135u3k000m7683/}}</ref>
==Publications==
{{Main|List of works by Nikolay Bogolyubov}}
===Books===
'''Mathematics and Non-linear Mechanics:'''
#[[Nikolay Mitrofanovich Krylov|N. M. Krylov]] and N. N. Bogoliubov (1934): ''On various formal expansions of non-linear mechanics''. Kiev, Izdat. Zagal'noukr. Akad. Nauk. {{uk icon}}
#[[Nikolay Mitrofanovich Krylov|N. M. Krylov]] and N. N. Bogoliubov (1947): ''Introduction to Nonlinear Mechanics.'' Princeton, Princeton University Press.
#N. N. Bogoliubov, [[Yurii Mitropolskiy|Y. A. Mitropolsky]] (1961): ''Asymptotic Methods in the Theory of Non-Linear Oscillations''. New York, Gordon and Breach.
'''Statistical Mechanics:'''
#N. N. Bogoliubov (1945): ''On Some Statistical Methods in Mathematical Physics''. Kyiv {{ru icon}}.
#N. N. Bogoliubov, V. V. Tolmachev, [[Dmitry Shirkov|D. V. Shirkov]] (1959): ''A New Method in the Theory of Superconductivity''. New York, Consultants Bureau.
#N. N. Bogoliubov (1960): ''Problems of Dynamic Theory in Statistical Physics''. Oak Ridge, Tenn., Technical Information Service.
#N. N. Bogoliubov (1967—1970): ''Lectures on Quantum Statistics. Problems of Statistical Mechanics of Quantum Systems''. New York, Gordon and Breach.
#N. N. Bogolubov and N. N. Bogolubov, Jnr. (1992): ''Introduction to Quantum Statistical Mechanics''. Gordon and Breach. ISBN 2-88124-879-9.
'''Quantum Field Theory:'''
#N. N. Bogoliubov, B. V. Medvedev, M. K. Polivanov (1958): ''Problems in the Theory of Dispersion Relations''. Institute for Advanced Study, Princeton.
#N. N. Bogoliubov, [[Dmitry Shirkov|D. V. Shirkov]] (1959): ''The Theory of Quantized Fields''. New York, Interscience. The first text-book on the [[renormalization group]] theory.
#N. N. Bogoliubov, A. A. Logunov and I. T. Todorov (1975): ''Introduction to Axiomatic Quantum Field Theory''.<ref>{{cite journal|author=Jaffee, Arthur|title=Review: N. N. Bogolubov, A. A. Logunov and I. T. Todorov, ''Introduction to axiomatic quantum field theory''|journal=Bull. Amer. Math. Soc.|year=1977|volume=83|issue=3|pages=349–351|url=http://projecteuclid.org/euclid.bams/1183538790|doi=10.1090/s0002-9904-1977-14261-4}}</ref> Reading, Mass.: W. A. Benjamin, Advanced Book Program. ISBN 978-0-8053-0982-9. ISBN 0-8053-0982-9.
#N. N. Bogoliubov, [[Dmitry Shirkov|D. V. Shirkov]] (1980): ''Introduction to the Theory of Quantized Field''. John Wiley & Sons Inc; 3rd edition. ISBN 0-471-04223-4. ISBN 978-0-471-04223-5.
#N. N. Bogoliubov, [[Dmitry Shirkov|D. V. Shirkov]] (1982): ''Quantum Fields''. Benjamin-Cummings Pub. Co., ISBN 0-8053-0983-7.
#N. N. Bogoliubov, A. A. Logunov, A. I. Oksak, I. T. Todorov (1990): ''General Principles of Quantum Field Theory''. Dordrecht [Holland]; Boston, Kluwer Academic Publishers. ISBN 0-7923-0540-X. ISBN 978-0-7923-0540-8.
;Selected works
#N. N. Bogoliubov, ''Selected Works. Part I. Dynamical Theory.'' Gordon and Breach, New York, 1990. ISBN 2-88124-752-0, ISBN 978-2-88124-752-1.
#N. N. Bogoliubov, ''Selected Works. Part II. Quantum and Classical Statistical Mechanics.'' Gordon and Breach, New York, 1991. ISBN 2-88124-768-7.
#N. N. Bogoliubov, ''Selected Works. Part III. Nonlinear Mechanics and Pure Mathematics.'' Gordon and Breach, Amsterdam, 1995. ISBN 2-88124-918-3.
#N. N. Bogoliubov, ''Selected Works. Part IV. Quantum Field Theory.'' Gordon and Breach, Amsterdam, 1995. ISBN 2-88124-926-4, ISBN 978-2-88124-926-6.
===Selected papers===
*{{cite journal | last1 = Bogoliubov | first1 = N. N. | year = 1948 | title = Equations of Hydrodynamics in Statistical Mechanics" (in Ukrainian) | url = | journal = Sbornik Trudov Instituta Matematiki AN USSR | volume = 10 | issue = | pages = 41–59 }}
*"On Question about Superfluidity Condition in the Nuclear Matter Theory" (in Russian), Doklady Akademii Nauk USSR, 119, 52, 1958.
* "On One Variational Principle in Many Body Problem" (in Russian), Doklady Akademii Nauk USSR, 119, N2, 244, 1959.
*"On Compensation Principle in the Method of Selfconformed Field" (in Russian), Uspekhi Fizicheskhih Nauk, 67, N4, 549, 1959.
*"The Quasi-averages in Problems of Statistical Mechanics" (in Russian), Preprint D-781, JINR, Dubna, 1961.
*"On the Hydrodynamics of a Superfluiding" (in Russian), Preprint P-1395, JINR, Dubna, 1963.
==See also==
*[[BBGKY hierarchy|Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy]]
*[[Bogoliubov causality condition]]
*[[Bogolyubov's edge-of-the-wedge theorem]]
*[[Bogoliubov inner product]]
*[[Bogoliubov-Parasyuk theorem]]
*[[Bogoliubov transformation]]
*[[Describing function|Describing function method]]
*[[Krylov-Bogoliubov averaging method]]
*[[Krylov-Bogolyubov theorem]]
==References==
{{Reflist|2}}
==Further reading==
*{{cite journal | last1 = Mitropolskiy | first1 = Yu. A. | authorlink = Yurii Mitropolskiy | authorlink2 = Sergei Tyablikov | last2 = Tyablikov | first2 = S. V. | year = 1959 | title = Nikolai Nikolaevich Bogolyubov (on the occasion of his fiftieth birthday) | doi = 10.1070/PU1959v002n05ABEH003172 | journal = Soviet Physics Uspekhi | volume = 2 | issue = 5| pages = 765–770 |bibcode = 1959SvPhU...2..765M }}
*{{cite journal | last1 = Zubarev | first1 = D. N. | authorlink = Dmitry Zubarev | display-authors = etal | year = 1970 | title = Nikolai Nikolaevich Bogolyubov (On his 60th birthday) | journal = Soviet Physics Uspekhi | volume = 12 | issue = 4| pages = 590–593 | doi=10.1070/PU1970v012n04ABEH003911|bibcode = 1970SvPhU..12..590Z }}
*{{cite journal | last1 = Vladimirov | first1 = V. S. | authorlink = Vasily Vladimirov | display-authors = etal | year = 1969 | title = Nikolai Nikolaevich Bogolyubov (on the occasion of his sixtieth birthday) | journal = Russian Math. Surveys | volume = 24 | issue = 4| pages = 167–175 | doi=10.1070/RM1969v024n04ABEH001356|bibcode = 1969RuMaS..24..167V }}
*{{cite journal | last1 = Ambartsumyan | first1 = V. A. | authorlink = Viktor Amazaspovich Ambartsumian | display-authors = etal | year = 1979 | title = Nikolai Nikolaevich Bogolyubov (on his seventieth birthday) | journal = Soviet Physics Uspekhi | volume = 22 | issue = 8| pages = 672–676 | doi=10.1070/PU1979v022n08ABEH005604|bibcode = 1979SvPhU..22..672A }}
*{{cite journal | last1 = Aleksandrov | first1 = P. S. | authorlink = Pavel Alexandrov | display-authors = etal | year = 1979 | title = Nikolai Nikolaevich Bogolyubov (on his seventieth birthday) | journal = Russian Math. Surveys | volume = 34 | issue = 5| pages = 1–10 | doi=10.1070/RM1979v034n05ABEH003905|bibcode = 1979RuMaS..34R...1A }}
*{{cite journal | last1 = Logunov | first1 = A. A. | authorlink2 = Sergei Novikov (mathematician) | last2 = Novikov | first2 = S. P. | last3 = Vladimirov | first3 = V. S. | year = 1989 | title = Nikolai Nikolaevich Bogolyubov (on his 80th birthday) | journal = Russian Math. Surveys | volume = 44 | issue = 5| pages = 1–10 | doi=10.1070/RM1989v044n05ABEH002280|bibcode = 1989RuMaS..44....1L }}
*{{cite journal | last1 = Abrikosov | first1 = A. A. | authorlink = Alexei Alexeyevich Abrikosov | display-authors = etal | year = 1989 | title = Nikolai Nikolaevich Bogolyubov (on his eightieth birthday) | journal = Soviet Physics Uspekhi | volume = 32 | issue = 12| pages = 1111–1112 | doi=10.1070/PU1989v032n12ABEH002785|bibcode = 1989SvPhU..32.1111A }}
*{{cite journal | last1 = Faddeev | first1 = L. D. | authorlink = Ludvig Faddeev | display-authors = etal | year = 1992 | title = Nikolai Nikolaevich Bogolyubov (obituary) | doi = 10.1070/RM1992v047n03ABEH000892 | journal = Russian Math. Surveys | volume = 47 | issue = 3| pages = 1–3 |bibcode = 1992RuMaS..47....1F }}
*{{cite journal | last1 = Anosov | first1 = D. V. | authorlink = Dmitri Anosov | year = 1994 | title = On the contribution of N.N. Bogolyubov to the theory of dynamical systems | journal = Russian Math. Surveys | volume = 49 | issue = 5| pages = 1–18 | doi=10.1070/RM1994v049n05ABEH002417|bibcode = 1994RuMaS..49....1A }}
*{{cite journal | last1 = Boglyubov | first1 = Nikolay | year = 1994 | title = N. N. Bogolyubov and statistical mechanics | doi = 10.1070/RM1994v049n05ABEH002419 | journal = Russian Math. Surveys | volume = 49 | issue = 5| pages = 19–49 |bibcode = 1994RuMaS..49...19B }}
*{{cite journal | last1 = Vladimirov | first1 = V. S. | last2 = Zharinov | first2 = V. V. | last3 = Sergeev | first3 = A. G. | year = 1994 | title = Bogolyubov's "edge of the wedge" theorem, its development and applications | journal = Russian Math. Surveys | volume = 49 | issue = 5| pages = 51–65 | doi=10.1070/RM1994v049n05ABEH002421|bibcode = 1994RuMaS..49...51V }}
*{{cite journal | last1 = Zav'yalov | first1 = O. I. | year = 1994 | title = Bogolyubov's R-operation and the Bogolyubov-Parasyuk theorem | journal = Russian Math. Surveys | volume = 49 | issue = 5| pages = 67–76 | doi=10.1070/RM1994v049n05ABEH002426|bibcode = 1994RuMaS..49...67Z }}
*{{cite journal | last1 = Levitan | first1 = B. M. | year = 1994 | title = On the work of Nikolai Nikolaevich Bogolyubov in the theory of almost periodic functions | journal = Russian Math. Surveys | volume = 49 | issue = 5| pages = 77–88 | doi=10.1070/RM1994v049n05ABEH002428|bibcode = 1994RuMaS..49...77L }}
*{{cite journal | last1 = Medvedev | first1 = B. V. | year = 1994 | title = N.N. Bogolyubov and the scattering matrix | journal = Russian Math. Surveys | volume = 49 | issue = 5| pages = 89–108 | doi=10.1070/RM1994v049n05ABEH002430|bibcode = 1994RuMaS..49...89M }}
*{{cite journal | last1 = Samoilenko | first1 = A. M. | year = 1994 | title = N.N. Bogolyubov and non-linear mechanics | journal = Russian Math. Surveys | volume = 49 | issue = 5| pages = 109–154 | doi=10.1070/RM1994v049n05ABEH002432|bibcode = 1994RuMaS..49..109S }}
*{{cite journal | last1 = Shirkov | first1 = D. V. | authorlink = Dmitry Shirkov | year = 1994 | title = The Bogoliubov renormalization group | url = http://arxiv.org/abs/hep-th/9602024 | journal = Russian Math. Surveys | volume = 49 | issue = 5| pages = 155–176 | doi=10.1070/rm1994v049n05abeh002434|bibcode = 1994RuMaS..49..155S }}
*{{cite journal | last1 = Vladimirov | first1 = V. S. | authorlink = Vasily Vladimirov | year = 2001 | title = N. N. Bogoliubov and mathematics | doi = 10.1070/RM2001v056n03ABEH000413 | journal = Russian Math. Surveys | volume = 56 | issue = 3| pages = 607–613 |bibcode = 2001RuMaS..56..607V }}
==External links==
*[http://www.bitp.kiev.ua/index.php?lang=en Bogolyubov Institute for Theoretical Physics] of the National Academy of Sciences of Ukraine.
*[http://itpm.msu.su/ Bogolyubov Institute for Theoretical Problems of Microphysics] at the [[Moscow State University|Lomonosov Moscow State University]], Russia.
*[http://theor.jinr.ru/ Bogolyubov Laboratory of Theoretical Physics] at the [[Joint Institute for Nuclear Research]], Dubna, Russia.
*[http://www.mi.ras.ru/index.php?c=show_dep&id=6&l=1&id=6 Department of Theoretical Physics] in the Steklov Mathematical Institute, Moscow, Russia (created by Nikolay Bogolyubov).
*[http://pravoslavie.dubna.ru/1/history.html The role of Nikolay Bogoliubov in Dubna's Russian Orthodox Christian church] (in Russian).
*{{MathGenealogy|id=76947}}
* [https://zbmath.org/authors/?q=ai:bogolyubov.nikolai-nikolaevich Author profile] in the database [[Zentralblatt MATH|zbMATH]]
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