V. V. Sokolov, “Integrable Hamiltonians related to the $\mathfrak{e}(3)$, $\mathfrak{so}(4)$, and $\mathfrak{so}(3,1)$ Poisson brackets”, Theoret. and Math. Phys., 223:2 (2025), 742–754
2.
D. I. Gurevich, P. A. Saponov, V. V. Sokolov, “On symmetrizers in quantum matrix algebras”, Russian Math. Surveys, 78:4 (2023), 785–787
3.
I. Bobrova, V. Sokolov, “Classification of Hamiltonian non-abelian Painlevé type systems”, Journal of Nonlinear Mathematical Physics, 30:2 (2023), 646–662
V. V. Sokolov, “Non-Abelian $\mathfrak{so}_3$ Euler top”, Russian Math. Surveys, 76:1 (2021), 183–185
7.
V. E. Adler, V. V. Sokolov, “Matrix Painlevé II equations”, Theoret. and Math. Phys., 207:2 (2021), 560–571
8.
V. V. Sokolov, I. P. Shestakov, “Multi-component generalizations of mKdV equation and nonassociative algebraic structures”, Journal of Algebra and its Applications, 20:4 (2021), 2150050
9.
V. E. Adler, V. V. Sokolov, “Non-Abelian Evolution Systems with Conservation Laws”, Mathematical physics analysis and geometry, 24:7 (2021)
V. V. Sokolov, “Integrable evolution systems of geometric type”, Theoret. and Math. Phys., 202:3 (2020), 428–436
13.
A. G. Meshkov, V. V. Sokolov, “Classification of integrable vector equations of geometric type”, Journal of Geometry and Physics, 149 (2020) https://doi.org/10.1016/j.geomphys.2019.103581
R. Hernandez Heredero, V. V. Sokolov, “The symmetry approach to integrability: recent advances”, Nonlinear Systems and Their Remarkable Mathematical Structures, 2, eds. N. Euler, M. C. Nucci, CRC Press, Boca Raton, 2019, 119–157
V. V. Sokolov, “Elliptic Calogero-Moser Hamiltonians and Compatible Poisson Brackets”, Recent Developments in Integrable Systems and Related Topics of Mathematical Physics (Kezenoi-Am, Russia, 2016), Springer Proceedings in Mathematics and Statistics, 273, eds. V. M. Buchstaber, S. Konstantinou-Rizos, A. V. Mikhailov, Springer, 2018, 38–46
V. V. Sokolov, A. B. Shabat, “Rational solutions of a Riccati equation”, Russian Math. Surveys, 71:4 (2016), 787–789
20.
V. V. Sokolov, “Algebraic quantum Hamiltonians on the plane”, Theoret. and Math. Phys., 184:1 (2015), 940–952
21.
V. V. Sokolov, A. V. Turbiner, “Quasi-exact-solvability of the A_2/G_2 elliptic model: algebraic form, sl(3)/g^{(2)} hidden algebra, and polynomial eigenfunctions”, Journal of Physics A: Mathematical and Theoretical, 48:15 (2015), 155201
A. M. Kamchatnov, V. V. Sokolov, “Nonlinear waves in two-component Bose-Einstein condensates: Manakov system and Kowalevski equations”, Physical Review A, 91:4 (2015), 043621
A. G. Meshkov, V. V. Sokolov, “Integrable Hamiltonian equations of fifth order with the Hamiltonian operator D_x”, Russian Journal of Mathematical Physics, 22:2 (2015), 201—214
24.
V. V. Sokolov, A. V. Turbiner, “Quasi-exact-solvability of the A_2/G_2 elliptic model: algebraic form, sl(3)/g^{(2)} hidden algebra, and polynomial eigenfunctions”, correction, Journal of Physics A: Mathematical and Theoretical, 48:35 (2015), 359501
A. Meshkov, V. Sokolov, “Vector hyperbolic equations on the sphere possessing Integrable third-order symmetries”, Letters in Mathematical Physics, 104:3 (2014), 341–360
A. V. Odesskii, V. N. Roubtsov, V. V. Sokolov, “Double Poisson brackets depending on parameters”, International Journal of Geometric Methods in Modern Physics, 11:9 (2014), 1460036
V. V. Sokolov, “Classification of constant solutions of the associative Yang–Baxter equation on $\operatorname{Mat}_3$”, Theoret. and Math. Phys., 176:3 (2013), 1156–1162
28.
A. V. Odesskii, V. N. Rubtsov, V. V. Sokolov, “Double Poisson brackets on free associative algebras”, Contemporary Mathematics, 592 (2013), 225–241
A. V. Odesskii, V. V. Sokolov, “Non-homogeneous systems of hydrodynamic type possessing Lax representations”, Communications in Mathematical Physics, 324:1 (2013), 47–62
A. V. Odesskii, V. N. Rubtsov, V. V. Sokolov, “Bi-Hamiltonian ordinary differential equations with matrix variables”, Theoret. and Math. Phys., 171:1 (2012), 442–447
31.
A. G. Meshkov, V. V. Sokolov, “Integrable evolution equations with a constant separant”, Ufimsk. Mat. Zh., 4:3 (2012), 104–154
32.
A. G. Meshkov, V. V. Sokolov, “Hyperbolic equations with third-order symmetries”, Theoret. and Math. Phys., 166:1 (2011), 43–57
33.
M. Dunajski, V. Sokolov, “On the 7th order ODE with submaximal symmetry”, Journal of Geometry and Physics, 61:8 (2011), 1258–1262
V. G. Marikhin, V. V. Sokolov, “Some integral equations related to random Gaussian processes”, Theoret. and Math. Phys., 164:2 (2010), 992–1001
35.
A. V. Odesskii, V. V. Sokolov, “Integrable $(2+1)$-dimensional systems of hydrodynamic type”, Theoret. and Math. Phys., 163:2 (2010), 549–586
36.
A. V. Odesskii, V. V. Sokolov, “Integrable pseudopotentials related to generalized hypergeometric functions”, Selecta Mathematica, 16:1 (2010), 145–172
A. V. Odesskii, V. V. Sokolov, “Classification of integrable hydrodynamic chains”, Journal of Physics A: Mathematical and Theoretical, 43:43 (2010), 434027
V. G. Marikhin, V. V. Sokolov, “Transformation of a pair of commuting Hamiltonians quadratic in momenta to canonical form and real partial separation of variables for the Clebsch top”, Regular and Chaotic Dynamics, 15:6 (2010), 652-–658
A. V. Odesskii, V. V. Sokolov, “Integrable elliptic pseudopotentials”, Theoret. and Math. Phys., 161:1 (2009), 1340–1352
40.
A. V. Mikhailov, V. V. Sokolov, “Symmetries of differential equations and the problem of Integrability”, Integrability, Lecture Notes in Physics, 767, eds. A. V. Mikhailov,, Springer, 2009, 19–88
E. V. Ferapontov, A. Moro, V. V. Sokolov, “Hamiltonian systems of hydrodynamic type in 2+1 dimensions”, Communications in Mathematical Physics, 285:1 (2009), 31–65
A. V. Odesskii, V. V. Sokolov, “On (2+1)-Dimensional Hydrodynamic Type Systems Possessing a Pseudopotential with Movable Singularities”, Funct. Anal. Appl., 42:3 (2008), 205–212
43.
V. G. Marikhin, V. V. Sokolov, “On the reduction of the pair of hamiltonians quadratic in momenta to canonic form and real partial separation of variables for the Clebsch top”, Nelin. Dinam., 4:3 (2008), 313–322
44.
V. V. Sokolov, S. Ya. Startsev, “Symmetries of nonlinear hyperbolic systems of the Toda chain type”, Theoret. and Math. Phys., 155:2 (2008), 802–811
45.
A. V. Odesskii, M. V. Pavlov, V. V. Sokolov, “Classification of integrable Vlasov-type equations”, Theoret. and Math. Phys., 154:2 (2008), 209–219
46.
D. K. Demskoy, V. V. Sokolov, “On recursion operators for elliptic models”, Nonlinearity, 21:6 (2008), 1253–1264
A. V. Odesskii, V. V. Sokolov, “Pairs of compatible associative algebras, classical Yang-Baxter equation and quiver representations”, Communications in Mathematical Physics, 278:1 (2008), 83–99
V. G. Marikhin, V. V. Sokolov, “Pairs of commuting Hamiltonians quadratic in the momenta”, Theoret. and Math. Phys., 149:2 (2006), 1425–1436
49.
I. Z. Golubchik, V. V. Sokolov, “Compatible Lie Brackets and the Yang–Baxter Equation”, Theoret. and Math. Phys., 146:2 (2006), 159–169
50.
A. V. Odesskii, V. V. Sokolov, “Integrable matrix equations related to pairs of compatible associative algebras”, Journal of Physics A: Mathematical and General, 39:40 (2006), 12447–12456
V. V. Sokolov, T. Wolf, “New integrable quadratic Hamiltonians on so(4) and so(3,1)”, Journal of Physics A: Mathematical and General, 39:8 (2006), 1915–1936
A. V. Odesskii, V. V. Sokolov, “Algebraic structures connected with pairs of compatible associative algebras”, International Mathematics Research Notices, 2006:9 (2006), 43734-43734
O. V. Efimovskaya, V. V. Sokolov, “Decompositions of the loop algebra over $\mathrm{so}(4)$ and integrable models of the chiral equation type”, J. Math. Sci., 136:6 (2006), 4385–4391
58.
I. Z. Golubchik, V. V. Sokolov, “Factorization of the Loop Algebra and Integrable Toplike Systems”, Theoret. and Math. Phys., 141:1 (2004), 1329–1347
59.
A. G. Meshkov, V. V. Sokolov, “Classification of Integrable Divergent $N$-Component Evolution Systems”, Theoret. and Math. Phys., 139:2 (2004), 609–622
60.
V. V. Sokolov, “On decompositions of the loop algebra over so(3) into a sum of two subalgebras”, Dokl. Math., 70:1 (2004), 568-570
61.
V. V. Sokolov, “One class of quadratic so(4) Hamiltonians”, Dokl. Math, 69:1 (2004), 108-111
62.
I. V. Komarov, V. V. Sokolov, A. V. Tsiganov, “Poisson maps and integrable deformations of Kowalevski top”, Journal of Physics A: Mathematical and General, 36:29 (2003), 8035–8047
I. Z. Golubchik, V. V. Sokolov, “Compatible Lie Brackets and Integrable Equations of the Principal Chiral Model Type”, Funct. Anal. Appl., 36:3 (2002), 172–181
65.
V. V. Sokolov, A. V. Tsiganov, “Commutative Poisson Subalgebras for Sklyanin Brackets and Deformations of Some Known Integrable Models”, Theoret. and Math. Phys., 133:3 (2002), 1730–1743
66.
V. V. Sokolov, A. V. Tsiganov, “Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops”, Theoret. and Math. Phys., 131:1 (2002), 543–549
67.
A. G. Meshkov, V. V. Sokolov, “Integrable evolution equations on the N-dimensional sphere”, Communications in Mathematical Physics, 232:1 (2002), 1–18.
V. V. Sokolov, “Generalized Kowalewski Top: new integrable cases on e(3) and so(4)”, Kowalevski property, CRM Proceedings and Lecture Notes, 32, eds. V .B. Kuznetsov, AMS, 2002, 307–313
A. V. Zhiber, V. V. Sokolov, “Exactly integrable hyperbolic equations of Liouville type”, Russian Math. Surveys, 56:1 (2001), 61–101
70.
V. V. Sokolov, “A New Integrable Case for the Kirchhoff Equation”, Theoret. and Math. Phys., 129:1 (2001), 1335–1340
71.
V. V. Sokolov, T. Wolf, “Classification of integrable polynomial vector evolution equations”, Journal of Physics A: Mathematical and General, 34 (2001), 11139-11148
I. Z. Golubchik, V. V. Sokolov, “One More Kind of the Classical Yang–Baxter Equation”, Funct. Anal. Appl., 34:4 (2000), 296–298
74.
I. Z. Golubchik, V. V. Sokolov, “Multicomponent generalization of the hierarchy of the Landau–Lifshitz equation”, Theoret. and Math. Phys., 124:1 (2000), 909–917
75.
A. V. Mikhailov, V. V. Sokolov, “Integrable ordinary differential equations on free associative algebras”, Theoret. and Math. Phys., 122:1 (2000), 72–83
76.
I, Z. Golubchik, V. V. Sokolov, “Generalized operator Yang-Baxter equations, integrable ODEs and nonassociative algebras”, Journal of Nonlinear Mathematical Physics, 7:2 (2000), 184-197
I. Z. Golubchik, V. V. Sokolov, “Generalized Heisenberg equations on $\mathbb Z$-graded Lie algebras”, Theoret. and Math. Phys., 120:2 (1999), 1019–1025
79.
A. V. Zhiber, V. V. Sokolov, “New example of a nonlinear hyperbolic equation possessing integrals”, Theoret. and Math. Phys., 120:1 (1999), 834–839
80.
M. Gürses, A. Karasu, V. V. Sokolov, “On construction of recursion operators from Lax representation”, Journal of Mathematical Physics, 40:12 (1999), 6473–6490
I. Z. Golubchik, V. V. Sokolov, “Integrable equations on $\mathbb Z$-graded Lie algebras”, Theoret. and Math. Phys., 112:3 (1997), 1097–1103
86.
I. Z. Golubchik, V. V. Sokolov, “On some generalizations of the factorization method”, Theoret. and Math. Phys., 110:3 (1997), 267–276
87.
I. Z. Golubchik, V. V. Sokolov, “Integrable Systems Generated by a Constant Solution of the Yang–Baxter Equation”, Funct. Anal. Appl., 30:4 (1996), 275–277
88.
S. I. Svinolupov, V. V. Sokolov, “Deformations of triple Jordan systems and integrable equations”, Theoret. and Math. Phys., 108:3 (1996), 1160–1163
89.
I. T. Habibullin, V. V. Sokolov, R. I . Yamilov, “Multi-component integrable systems and nonassociative structures”, Nonlinear Physics: Theory and Experiment, 95 (1996), 139–168
90.
V. V. Sokolov, A. V. Zhiber, “On the Darboux integrable hyperbolic equations”, Physics Letters A, 208:4-6 (1995), 303-308
V. V. Sokolov, S. I. Svinolupov, “Deformation of nonassociative algebras and integrable differential equations”, Acta Applicandae Mathematica, 41:1-2 (1995), 323–339
R. Hern{ a}ndez, V. V. Sokolov, S. I. Svinolupov, “Classification of third order integrable evolution equations”, Physica D: Nonlinear Phenomena, 87:1-4 (1995), 32–36
V. V. Sokolov, S. I. Svinolupov, “On nonclassical invertible transformations of hyperbolic equations”, European Journal of Applied Mathematics, 6:2 (1995), 145-156
A. V. Zhiber, V. V. Sokolov, S. Ya. Startsev, “Darboux integrable nonlinear hyperbolic equations”, Dokl. Math., 52:1 (1995), 128-130
95.
S. I. Svinolupov, V. V. Sokolov, “Vector-matrix generalizations of classical integrable equations”, Theoret. and Math. Phys., 100:2 (1994), 959–962
96.
R H. Heredero, V. V. Sokolov, S. I. Svinolupov, “Toward the classification of third-order integrable evolution equations”, Journal of Physics A: Mathematical and General, 27:13 (1994), 4557-4568
S. I. Svinolupov, V. V. Sokolov, “Representations of contragradient Lie algebras in contact vector fields”, Funct. Anal. Appl., 25:2 (1991), 146–147
101.
A. V. Mikhailov, A. B. Shabat, V. V. Sokolov, “The symmetry approach to classification of integrable equations”, What is integrability?, Springer series in nonlinear dynamics, eds. V. E. Zakharov, Springer, Berlin, Heidelberg, 1991, 115-184
S. I. Svinolupov, V. V. Sokolov, “Weak nonlocalities in evolution equations”, Math. Notes, 48:6 (1990), 1234–1239
103.
V. V. Sokolov, “Pseudosymmetries and differential substitutions”, Funct. Anal. Appl., 22:2 (1988), 121–129
104.
V. V. Sokolov, “On the symmetries of evolution equations”, Russian Math. Surveys, 43:5 (1988), 165–204
105.
F. Kh. Mukminov, V. V. Sokolov, “Integrable evolution equations with constraints”, Math. USSR-Sb., 61:2 (1988), 389–410
106.
V. V. Sokolov, “On the structure of the algebra of symmetries for a one-field evolution equation”, Sov. Math., Dokl., 35:3 (1987), 635-638
107.
V. V. Sokolov, “Quasienergy integral for canonical maps”, Theoret. and Math. Phys., 67:2 (1986), 464–473
108.
V. G. Drinfeld, V. V. Sokolov, “Equations that are related to the Korteweg-de Vries equation”, Dokl. Akad. Nauk SSSR, 284:1 (1985), 29–33
109.
V. G. Drinfeld, S. I. Svinolupov, V. V. Sokolov, “Klassifikatsiya evolyutsionnykh uravnenii pyatogo poryadka, obladayuschikh beskonechnoi seriei zakonov sokhraneniya”, Doklady AN USSR, A10 (1985), 7-10
110.
V. V. Sokolov, “Hamiltonian property of the Krichever-Novikov equation”, Dokl. Akad. Nauk SSSR, 277:1 (1984), 48–50
111.
V. G. Drinfeld, V. V. Sokolov, “Lie algebras and equations of Korteweg–de Vries type”, J. Soviet Math., 30:2 (1985), 1975–2036
112.
V. V. Sokolov, A. B. Shabat, “Classification of integrable evolution equations”, Mathematical physics reviews, 4 (1984), 221-280
113.
V. V. Sokolov, “On the nature of the quantum corrections in the case of stochastic motion of a nolinear oscillator”, Theoret. and Math. Phys., 61:1 (1984), 1041–1048
114.
V. V. Sokolov, “Moments of the distributio function and kinetic equation for stochastic motion of a nonlinear oscillator”, Theoret. and Math. Phys., 59:1 (1984), 396–403
115.
S. I. Svinolupov, V. V. Sokolov, R. I. Yamilov, “On Bäcklund transformations for integrable evolution equations”, Dokl. Akad. Nauk SSSR, 271:4 (1983), 802–805
116.
S. I. Svinolupov, V. V. Sokolov, “Evolution equations with nontrivial conservative laws”, Funct. Anal. Appl., 16:4 (1982), 317–319
117.
V. G. Drinfeld, V. V. Sokolov, “Equations of Korteweg–de Vries type, and simple Lie algebras”, Dokl. Akad. Nauk SSSR, 258:1 (1981), 11–16
118.
V. G. Drinfeld, V. V. Sokolov, “Novye evolyutsionnye uravneniya, obladayuschie L,A-paroi”, Trudy seminara S. L. Soboleva, 2:1 (1981), 5-9
119.
V. V. Sokolov, A. B. Shabat, “$(L,A)$-Pairs and a Ricatti type substitution”, Funct. Anal. Appl., 14:2 (1980), 148–150
120.
V. V. Sokolov, “Birationally isomorphic commutative rings of differential operators”, Funct. Anal. Appl., 12:3 (1978), 234–236
121.
V. V. Sokolov, “Examples of commutative rings of differential operators”, Funct. Anal. Appl., 12:1 (1978), 65–66
122.
V. V. Sokolov, “Adiabatic perturbation theory for quasilevels”, Theoret. and Math. Phys., 35:3 (1978), 499–507
Books
123.
Vladimir Sokolov, Algebraic Structures in Integrability, World Scientific, Singapore, 2020 , 327 pp.
124.
V. V. Sokolov, Algebraicheskie struktury v teorii integriruemykh sistem, 1-e izd., eds. V. Kats, Institut kompyuternykh issledovanii, M.–Izhevsk :, 2019 , 368 pp.
Preprints
125.
A. V. Bocharov, V. V. Sokolov, S. I. Svinolupov, On some equivalence problems for differential equations, Preprint № 54, Erwin Schrodinger Institute for Mathematical Physics, Vienna, 1993 , 12 pp.
Personalia
126.
V. E. Adler, P. Winternitz, R. N. Garifullin, A. V. Zhiber, D. Levi, A. V. Mikhailov, I. Kh. Musin, F. W. Nijhoff, V. V. Sokolov, B. I. Suleimanov, E. V. Ferapontov, A. P. Fordy, I. T. Habibullin, I. Yu. Cherdantsev, R. A. Sharipov, R. S. Yulmukhametov, “In memory of Yamilov Ravil Islamovich”, Ufa Math. J., 12:3 (2020), 119–120
127.
L. M. Barkov, A. E. Bondar, N. S. Dikanskii, G. I. Dimov, È. P. Kruglyakov, G. N. Kulipanov, I. N. Meshkov, V. V. Parkhomchuk, A. N. Skrinsky, V. V. Sokolov, V. S. Fadin, I. B. Khriplovich, “In memory of Boris Valerianovich Chirikov”, Phys. Usp., 51:4 (2008), 423–424
128.
V. N. Baier, L. M. Barkov, A. E. Bondar, N. S. Dikanskii, V. F. Dmitriev, M. S. Zolotorev, È. P. Kruglyakov, G. N. Kulipanov, A. N. Skrinsky, V. V. Sokolov, V. S. Fadin, B. V. Chirikov, “Iosif Bentsionovich Khriplovich (on his seventieth birthday)”, Phys. Usp., 50:2 (2007), 219
129.
Drinfel’d, V. G., Sokolov, V. V., “Equations of Korteweg-de Vries type and simple Lie algebras”, Sov. Math., Dokl., 23 (1981), 457-462
Интегрируемые случаи на $е_3$ и $so(4)$ V. V. Sokolov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) July 19, 2023 14:00
9.
О матричных уравнениях Пенлеве V. V. Sokolov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) August 10, 2022 14:00
Интегрируемые гиперболические системы лиувиллевского типа V. V. Sokolov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) August 14, 2019 15:00
Интегрируемые 3D-системы гидродинамического типа V. V. Sokolov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) March 28, 2007
Коммутирующие гамильтонианы, квадратичные по моментам V. V. Sokolov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) October 5, 2005
