asymptotics,
semiclassical and adiabatic approximations,
waves,
vortices,
inhomogeneous media.
Subject:
Asymptotic and operator methods, mathematical physics, equations of quantum and continuum mechanics, low-dimensional structures and waveguides, homogenization
Biography
In 1967 I graduated from the school. N 2 in Moscow.
In 1967-1973 I studied at the Faculty of Applied Mathematics at the Moscow Institute of Electronic Engineering.
In 1973-1987, I studied in graduate school and worked in various positions at the Department of Applied Mathematics at the Kuibyshev Moscow Institute of Civil Engineering.
In 1977 I defended my PhD thesis in the specialty mathematical physics (adviser V.P.Maslov)
Since 1987, I have been working at the Ishlinsky Institute for Problems in Mechanical of the Russian Academy of Sciences, currently Chief Researcher and Head of the Laboratory.
In 1989, I defended my doctoral dissertation in the specialty mathematical physics.
Since 2006, I have been a part-time Head of the Department of Mathematics and Mathematical Methods of Physics at the Moscow Institute of Physics an Technology. Since 1973, I have been lecturing on general and special mathematical courses. In particular, in various years I taught special courses on asymptotic methods at Moscow Institute of Physics and Technology and at the Physical and Mechanical-Mathematical Faculties of Lomonosov Moscow State University. 13 people defended their PhD theses under my supervision, 3 of them are now doctors of science. I have participated and continue to participate, usually as a supervisor or coordinator, in various Russian scientific projects and scientific projects of other countries.I have more than 220 scientific publications.
Main publications:
1)S. Yu. Dobrokhotov, V. P. Maslov, “Finite-zone almost periodic solutions in WKB-approximations”, J. Soviet Math., 16:6 (1981), 1433–1487
2) V. V. Belov, S. Yu. Dobrokhotov, “Semiclassical Maslov asymptotics with complex phases. I. General approach”, Theoret. and Math. Phys., 92:2 (1992), 843–868
3)V. V. Belov, S. Yu. Dobrokhotov, T. Ya. Tudorovskiy, “Operator separation of variables for adiabatic problems in quantum and wave mechanics”, J. Eng. Math., 55:1-4 (2006) 183-237
4)S. Yu. Dobrokhotov, A.I.Shafarevich, B.Tirozzi, “Localized Wave and Vortical Solutions to Linear Hyperbolic Systems and Their Application to the Linear Shallow Water Equation”, Russ.J.Math.Phys. 15: 2,(2008), 192-221
5) S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “New integral representations of the Maslov canonical operator in singular charts”, Izv. Math., 81:2 (2017), 286–328
S. Yu. Dobrokhotov, A. V. Tsvetkova, “Dynamics of three-dimensional localized wave packets defined by the spherical Bessel function $\mathbf{j}_0(x)$”, TMF, 226:3 (2026), 574–600; Theoret. and Math. Phys., 226:3 (2026), 499–522
2.
I. A. Bogaevsky, S. Yu. Dobrokhotov, A. A. Tolchennikov, “The effect of changing the multiplicity of terms in the Cauchy problem for the
Dirac equation in graphene with a constant electric field and
a localized initial condition.”, TMF, 226:2 (2026), 256–276; Theoret. and Math. Phys., 226:2 (2026), 217–235
2025
3.
S. Yu. Dobrokhotov, S. B. Levin, A. A. Tolchennikov, “Global uniform asymptotics in the form of Airy functions for the problem of scattering on a repulsive Coulomb potential, and Keplerian trajectories”, Mat. Sb., 216:8 (2025), 112–128; Sb. Math., 216:8 (2025), 1121–1137
4.
S. Yu. Dobrokhotov, V. E. Nazaikinskii, I. A. Nosikov, A. A. Tolchennikov, “Asymptotics of long waves generated by time-harmonic spatially localized sources in basins with gently sloping shores”, Zh. Vychisl. Mat. Mat. Fiz., 65:5 (2025), 625–640; Comput. Math. Math. Phys., 65:5 (2025), 966–981
5.
S. Yu. Dobrokhotov, I. A. Nosikov, A. A. Tolchennikov, “The Jacobi–Maupertuis principle and Fermat variational principle in the problem of short-wave asymptotics in the solution of the Helmholtz equation with a localized source”, Zh. Vychisl. Mat. Mat. Fiz., 65:4 (2025), 446–459; Comput. Math. Math. Phys., 65:4 (2025), 739–753
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Averaging method for problems on quasiclassical asymptotics”, CMFD, 70:1 (2024), 53–76; Journal of Mathematical Sciences, 286:1 (2024), 46–67
7.
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “On the arguments of Jacobians in local expressions of the Maslov canonical operator”, Math. Notes, 116:6 (2024), 1264–1276
8.
S. Yu. Dobrokhotov, A. A. Tolchennikov, “Uniform formulas for the asymptotic solution near the leading front for Maxwell's equations with temporal dispersion and localized initial data”, Mat. Zametki, 116:3 (2024), 388–395; Math. Notes, 116:3 (2024), 458–464
M. M. Votiakova, S. Yu. Dobrokhotov, D. S. Minenkov, “Classical and Wave Dynamics of Long Nonlinear Waves Localized in the Vicinity of Gently Sloping Shores”, Trudy Mat. Inst. Steklova, 327 (2024), 27–43; Proc. Steklov Inst. Math., 327 (2024), 20–36
I. A. Bogaevsky, S. Yu. Dobrokhotov, A. A. Tolchennikov, “Arnold Lagrangian singularity in the asymptotics of the solution of a model two-dimensional Helmholtz equation with a localized right-hand side”, TMF, 218:1 (2024), 23–47; Theoret. and Math. Phys., 218:1 (2024), 19–40
S. Yu. Dobrokhotov, S. B. Levin, A. A. Tolchennikov, “Keplerian orbits and global asymptotic solution in the form of an Airy function for the scattering problem on a repulsive Coulomb potential”, Uspekhi Mat. Nauk, 78:4(472) (2023), 205–206; Russian Math. Surveys, 78:4 (2023), 788–790
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Nonlinear Effects and Run-up of Coastal Waves Generated by Billiards with Semi-rigid Walls in the Framework of Shallow Water Theory”, Trudy Mat. Inst. Steklova, 322 (2023), 111–123; Proc. Steklov Inst. Math., 322 (2023), 105–117
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, M. Rouleux, “Lagrangian manifolds and the construction of asymptotics for (pseudo)differential equations with localized right-hand sides”, TMF, 214:1 (2023), 3–29; Theoret. and Math. Phys., 214:1 (2023), 1–23
A. I. Aptekarev, S. Yu. Dobrokhotov, D. N. Tulyakov, A. V. Tsvetkova, “Plancherel–Rotach type asymptotic formulae for multiple orthogonal Hermite polynomials and
recurrence relations”, Izv. RAN. Ser. Mat., 86:1 (2022), 36–97; Izv. Math., 86:1 (2022), 32–91
A. Yu. Anikin, S. Yu. Dobrokhotov, A. A. Shkalikov, “On Expansions in the Exact and Asymptotic Eigenfunctions of the One-Dimensional Schrödinger Operator”, Mat. Zametki, 112:5 (2022), 644–664; Math. Notes, 112:5 (2022), 623–641
A. Yu. Anikin, S. Yu. Dobrokhotov, I. A. Nosikov, “Librations with large periods in tunneling: Efficient calculation and applications to trigonal dimers”, TMF, 213:1 (2022), 163–190; Theoret. and Math. Phys., 213:1 (2022), 1453–1476
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for two-dimensional standing coastal waves”, Algebra i Analiz, 33:2 (2021), 5–34; St. Petersburg Math. J., 33:2 (2022), 185–205
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations”, Uspekhi Mat. Nauk, 76:5(461) (2021), 3–80; Russian Math. Surveys, 76:5 (2021), 745–819
S. Yu. Dobrokhotov, D. S. Minenkov, V. E. Nazaikinskii, “Representations of Bessel functions via the Maslov canonical operator”, TMF, 208:2 (2021), 196–217; Theoret. and Math. Phys., 208:2 (2021), 1018–1037
S. Yu. Dobrokhotov, H. H. Ilyasov, O. L. Tolstova, “Simple Solutions to the Linear Problem of the Generation of Long Waves on the Surface of a Liquid by a Source in an Elastic Foundation Bottom”, Izvestiya RAN, MTT, 2020, no. 4, 126–139; Mechanics of Solids, 55:4 (2020), 561–572
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Lagrangian Manifolds and Efficient Short-Wave Asymptotics in a Neighborhood of a Caustic Cusp”, Mat. Zametki, 108:3 (2020), 334–359; Math. Notes, 108:3 (2020), 318–338
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Uniformization of Equations with Bessel-Type Boundary Degeneration and Semiclassical Asymptotics”, Mat. Zametki, 107:5 (2020), 780–786; Math. Notes, 107:5 (2020), 847–853
A. Yu. Anikin, S. Yu. Dobrokhotov, A. V. Tsvetkova, “Airy function and transition between the semiclassical and harmonic oscillator approximations for one-dimensional bound states”, TMF, 204:2 (2020), 171–180; Theoret. and Math. Phys., 204:2 (2020), 984–992
S. Yu. Dobrokhotov, M. V. Klimenko, I. A. Nosikov, A. A. Tolchennikov, “Variational method for computing ray trajectories and fronts of tsunami waves generated by a localized source”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1439–1448; Comput. Math. Math. Phys., 60:8 (2020), 1392–1401
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Efficient asymptotics in problems on the propagation of waves generated by localized sources in linear multidimensional inhomogeneous and dispersive media”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1394–1407; Comput. Math. Math. Phys., 60:8 (2020), 1348–1360
S. Yu. Dobrokhotov, Kh. Kh. Ilyasov, S. Ya. Sekerzh-Zenkovich, O. L. Tolstova, “Simple solutions to the wave problem on the surface of a fluid with the linear hydroelastic model”, Dokl. Akad. Nauk, 487:4 (2019), 370–375; Doklady Physics, 64:8 (2019), 319–324
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Asymptotic eigenfunctions of the operator $\nabla D(x)\nabla$ defined in a two-dimensional domain and degenerating on its boundary and billiards with semi-rigid walls”, Differ. Uravn., 55:5 (2019), 660–672; Differ. Equ., 55:5 (2019), 644–657
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Asymptotics, Related to Billiards with Semi-Rigid Walls, of Eigenfunctions of the $\nabla D(x)\nabla$ Operator in Dimension 2 and Trapped Coastal Waves”, Mat. Zametki, 105:5 (2019), 792–797; Math. Notes, 105:5 (2019), 789–794
Sergei Yu. Dobrokhotov, Dmitrii S. Minenkov, Anatoly I. Neishtadt, Semen B. Shlosman, “Classical and Quantum Dynamics of a Particle in a Narrow Angle”, Regul. Chaotic Dyn., 24:6 (2019), 704–716
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Nonstandard Lagrangian Singularities and Asymptotic Eigenfunctions of the Degenerating Operator $-\frac{d}{dx}D(x)\frac{d}{dx}$”, Trudy Mat. Inst. Steklova, 306 (2019), 83–99; Proc. Steklov Inst. Math., 306 (2019), 74–89
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems”, TMF, 201:3 (2019), 382–414; Theoret. and Math. Phys., 201:3 (2019), 1742–1770
P. N. Petrov, S. Yu. Dobrokhotov, “Asymptotic solution of the Helmholtz equation in a three-dimensional layer of variable thickness with a localized right-hand side”, Zh. Vychisl. Mat. Mat. Fiz., 59:4 (2019), 566–578; Comput. Math. Math. Phys., 59:4 (2019), 529–541
Anatoly Anikin, Sergey Dobrokhotov, Vladimir Nazaikinskii, “Asymptotic solutions of the wave equation with degenerate velocity and with right-hand side localized in space and time”, Zh. Mat. Fiz. Anal. Geom., 14:4 (2018), 393–405
A. V. Aksenov, S. Yu. Dobrokhotov, K. P. Druzhkov, “Exact Step-Like Solutions of One-Dimensional Shallow-Water Equations over a Sloping Bottom”, Mat. Zametki, 104:6 (2018), 930–936; Math. Notes, 104:6 (2018), 915–921
S. Yu. Dobrokhotov, A. V. Tsvetkova, “Lagrangian Manifolds Related to the Asymptotics of Hermite Polynomials”, Mat. Zametki, 104:6 (2018), 835–850; Math. Notes, 104:6 (2018), 810–822
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Simple Asymptotics for a Generalized Wave Equation with Degenerating Velocity and Their Applications in the Linear Long Wave Run-Up Problem”, Mat. Zametki, 104:4 (2018), 483–504; Math. Notes, 104:4 (2018), 471–488
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “One Approach to the Computation of Asymptotics of Integrals of Rapidly Varying Functions”, Mat. Zametki, 103:5 (2018), 680–692; Math. Notes, 103:5 (2018), 33–43
S. Yu. Dobrokhotov, O. L. Tolstova, S. Ya. Sekerzh-Zenkovich, C. A. Vargas, “Influence of the Elastic Base of a Basin on the Propagation of Waves on the Water Surface”, Russ. J. Math. Phys., 25:4 (2018), 459–469
S. Yu. Dobrokhotov, D. S. Minenkov, S. B. Shlosman, “Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber”, TMF, 197:2 (2018), 269–278; Theoret. and Math. Phys., 197:2 (2018), 1626–1634
A. Yu. Anikin, S. Yu. Dobrokhotov, A. I. Klevin, B. Tirozzi, “Gausian packets and beams with focal points in vector problems of plasma physics”, TMF, 196:1 (2018), 135–160; Theoret. and Math. Phys., 196:1 (2018), 1059–1081
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “New integral representations of the Maslov canonical operator in singular charts”, Izv. RAN. Ser. Mat., 81:2 (2017), 53–96; Izv. Math., 81:2 (2017), 286–328
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “On the Asymptotics of a Bessel-Type Integral Having Applications in Wave Run-Up Theory”, Mat. Zametki, 102:6 (2017), 828–835; Math. Notes, 102:6 (2017), 756–762
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Punctured Lagrangian manifolds and asymptotic solutions of linear water wave equations with localized initial conditions”, Mat. Zametki, 101:6 (2017), 936–943; Math. Notes, 101:6 (2017), 1053–1060
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. A. Tolchennikov, “Uniform Asymptotics of the Boundary Values of the Solution in a Linear Problem on the Run-Up of Waves on a Shallow Beach”, Mat. Zametki, 101:5 (2017), 700–715; Math. Notes, 101:5 (2017), 802–814
A. Yu. Anikin, S. Yu. Dobrokhotov, A. I. Klevin, B. Tirozzi, “Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics”, TMF, 193:3 (2017), 409–433; Theoret. and Math. Phys., 193:3 (2017), 1761–1782
V. P. Maslov, S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Volume and Entropy in Abstract Analytic Number Theory and Thermodynamics”, Mat. Zametki, 100:6 (2016), 855–867; Math. Notes, 100:6 (2016), 828–834
S. Yu. Dobrokhotov, A. Yu. Anikin, “Approximation of Solutions of the Two-Dimensional Wave Equation with Variable Velocity and Localized Right-Hand Side Using Some “Simple” Solutions”, Mat. Zametki, 100:6 (2016), 825–837; Math. Notes, 100:6 (2016), 796–806
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Characteristics with Singularities and the Boundary Values of the Asymptotic Solution of the Cauchy Problem for a Degenerate Wave Equation”, Mat. Zametki, 100:5 (2016), 710–731; Math. Notes, 100:5 (2016), 695–713
A. Yu. Anikin, S. Yu. Dobrokhotov, M. I. Katsnel'son, “Lower part of the spectrum for the two-dimensional Schrödinger operator periodic in one variable and application to quantum dimers”, TMF, 188:2 (2016), 288–317; Theoret. and Math. Phys., 188:2 (2016), 1210–1235
J. Brüning, S. Yu. Dobrokhotov, M. I. Katsnel'son, D. S. Minenkov, “Semiclassical asymptotic approximations and the density of states for the two-dimensional radially symmetric Schrödinger and Dirac equations in tunnel microscopy problems”, TMF, 186:3 (2016), 386–400; Theoret. and Math. Phys., 186:3 (2016), 333–345
A. Yu. Anikin, J. Brüning, S. Yu. Dobrokhotov, “Averaging and trajectories of a Hamiltonian system appearing in graphene placed in a strong magnetic field and a periodic potential”, Fundam. Prikl. Mat., 20:2 (2015), 5–20; J. Math. Sci., 223:6 (2017), 656–666
S. Yu. Dobrokhotov, D. S. Minenkov, M. Rouleux, “The Maupertuis–Jacobi Principle for Hamiltonians of the Form $F(x,|p|)$ in Two-Dimensional Stationary Semiclassical Problems”, Mat. Zametki, 97:1 (2015), 48–57; Math. Notes, 97:1 (2015), 42–49
V. V. Grushin, S. Yu. Dobrokhotov, “Homogenization in the Problem of Long Water Waves over a Bottom Site with Fast Oscillations”, Mat. Zametki, 95:3 (2014), 359–375; Math. Notes, 95:3 (2014), 324–337
S. Yu. Dobrokhotov, G. N. Makrakis, V. E. Nazaikinskii, “Maslov's canonical operator, Hörmander's formula, and localization of the Berry–Balazs solution in the theory of wave beams”, TMF, 180:2 (2014), 162–188; Theoret. and Math. Phys., 180:2 (2014), 894–916
Yu. A. Chirkunov, S. Yu. Dobrokhotov, S. B. Medvedev, D. S. Minenkov, “Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms”, TMF, 178:3 (2014), 322–345; Theoret. and Math. Phys., 178:3 (2014), 278–298
S. Yu. Dobrokhotov, S. B. Medvedev, D. S. Minenkov, “On Replacements Reducing One-Dimensional Systems of Shallow-Water Equations to the Wave Equation with Sound Speed $c^2=x$”, Mat. Zametki, 93:5 (2013), 716–727; Math. Notes, 93:5 (2013), 704–714
V. V. Grushin, S. Yu. Dobrokhotov, S. A. Sergeev, “Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source”, Trudy Mat. Inst. Steklova, 281 (2013), 170–187; Proc. Steklov Inst. Math., 281 (2013), 161–178
S. Yu. Dobrokhotov, G. N. Makrakis, V. E. Nazaikinskii, T. Ya. Tudorovskii, “New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics”, TMF, 177:3 (2013), 355–386; Theoret. and Math. Phys., 177:3 (2013), 1579–1605
J. Brüning, S. Yu. Dobrokhotov, R. V. Nekrasov, “Splitting of lower energy levels in a quantum double well in a magnetic field and tunneling of wave packets in nanowires”, TMF, 175:2 (2013), 206–225; Theoret. and Math. Phys., 175:2 (2013), 620–636
J. Brüning, V. V. Grushin, S. Yu. Dobrokhotov, “Averaging of Linear Operators, Adiabatic Approximation, and Pseudodifferential Operators”, Mat. Zametki, 92:2 (2012), 163–180; Math. Notes, 92:2 (2012), 151–165
J. Brüning, V. V. Grushin, S. Yu. Dobrokhotov, T. Ya. Tudorovskii, “Generalized Foldy–Wouthuysen transformation and pseudodifferential operators”, TMF, 167:2 (2011), 171–192; Theoret. and Math. Phys., 167:2 (2011), 547–566
S. Yu. Dobrokhotov, D. S. Minenkov, “Remark on the phase shift in the Kuzmak–Whitham ansatz”, TMF, 166:3 (2011), 350–365; Theoret. and Math. Phys., 166:3 (2011), 303–316
S. Yu. Dobrokhotov, V. E. Nazaĭkinskiĭ, B. Tirozzi, “Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data”, Algebra i Analiz, 22:6 (2010), 67–90; St. Petersburg Math. J., 22:6 (2011), 895–911
S. Yu. Dobrokhotov, S. Ya. Sekerzh-Zen'kovich, “A Class of Exact Algebraic Localized Solutions of the Multidimensional Wave Equation”, Mat. Zametki, 88:6 (2010), 942–945; Math. Notes, 88:6 (2010), 894–897
V. V. Grushin, S. Yu. Dobrokhotov, “Peierls Substitution and the Maslov Operator Method”, Mat. Zametki, 87:4 (2010), 554–571; Math. Notes, 87:4 (2010), 521–536
S. Yu. Dobrokhotov, M. Rouleux, “The Semiclassical Maupertuis–Jacobi Correspondence and Applications to Linear Water Waves Theory”, Mat. Zametki, 87:3 (2010), 458–463; Math. Notes, 87:3 (2010), 430–435
J. Brüning, S. Yu. Dobrokhotov, R. V. Nekrasov, A. I. Shafarevich, “Propagation of Gaussian wave packets in thin periodic quantum
waveguides with a nonlocal nonlinearity”, TMF, 155:2 (2008), 215–235; Theoret. and Math. Phys., 155:2 (2008), 689–707
S. Yu. Dobrokhotov, B. Tirozzi, A. I. Shafarevich, “Representations of Rapidly Decreasing Functions by the Maslov Canonical Operator”, Mat. Zametki, 82:5 (2007), 792–796; Math. Notes, 82:5 (2007), 713–717
J. Brüening, S. Yu. Dobrokhotov, E. S. Semenov, “Unstable closed trajectories, librations and splitting of the lowest eigenvalues in quantum double well problem”, Regul. Chaotic Dyn., 11:2 (2006), 167–180
S. A. Albeverio, S. Yu. Dobrokhotov, M. A. Poteryakhin, “Non-Self-Adjointness of Operators with Small Diffusion”, Mat. Zametki, 78:6 (2005), 941–942; Math. Notes, 78:6 (2005), 874–876
72.
S. Yu. Dobrokhotov, E. S. Semenov, B. Tirozzi, “Hugoniot–Maslov Chains for the System of Shallow-Water Equations Taking into Account Energy Exchange”, Mat. Zametki, 78:5 (2005), 796–799; Math. Notes, 78:5 (2005), 740–743
V. V. Belov, S. Yu. Dobrokhotov, V. P. Maslov, T. Ya. Tudorovskii, “A generalized adiabatic principle for electron dynamics in curved nanostructures”, UFN, 175:9 (2005), 1004–1010; Phys. Usp., 48:9 (2005), 962–968
S. Yu. Dobrokhotov, M. A. Poteryakhin, “Normal Forms near Two-Dimensional Resonance Tori for the Multidimensional Anharmonic Oscillator”, Mat. Zametki, 76:5 (2004), 701–713; Math. Notes, 76:5 (2004), 653–664
V. V. Belov, S. Yu. Dobrokhotov, T. Ya. Tudorovskii, “Asymptotic Solutions of Nonrelativistic Equations of Quantum Mechanics in Curved Nanotubes: I. Reduction to Spatially One-Dimensional Equations”, TMF, 141:2 (2004), 267–303; Theoret. and Math. Phys., 141:2 (2004), 1562–1592
S. Yu. Dobrokhotov, E. S. Semenov, B. Tirozzi, “Calculation of Integrals of the Hugoniot–Maslov Chain for Singular Vortical Solutions of the Shallow-Water Equation”, TMF, 139:1 (2004), 62–76; Theoret. and Math. Phys., 139:1 (2004), 500–512
S. A. Albeverio, S. Yu. Dobrokhotov, E. S. Semenov, “Formation time of quark–gluon plasma in heavy-ion collisions in the holographic shock wave model”, TMF, 138:1 (2004), 116–126; Theoret. and Math. Phys., 138:1 (2004), 98–106
S. Yu. Dobrokhotov, E. S. Semenov, B. Tirozzi, “Hugoniót–Maslov Chains for Singular Vortical Solutions to Quasilinear Hyperbolic Systems and Typhoon Trajectory”, CMFD, 2 (2003), 5–44; Journal of Mathematical Sciences, 124:5 (2004), 5209–5249
J. Brüning, S. Yu. Dobrokhotov, V. A. Geiler, K. Pankrashkin, “Hall conductivity of minibands lying at the wings of Landau levels”, Pis'ma v Zh. Èksper. Teoret. Fiz., 77:11 (2003), 743–746; JETP Letters, 77:11 (2003), 616–618
V. V. Belov, S. Yu. Dobrokhotov, S. O. Sinitsyn, “Asymptotic solutions of the Schrödinger equation in thin tubes”, Trudy Inst. Mat. i Mekh. UrO RAN, 9:1 (2003), 15–25; Proc. Steklov Inst. Math., 2003, suppl. 1, S13–S23
V. V. Belov, S. Yu. Dobrokhotov, V. A. Maksimov, “Explicit Formulas for Generalized Action–Angle Variables in a Neighborhood of an Isotropic Torus and Their Application”, TMF, 135:3 (2003), 378–408; Theoret. and Math. Phys., 135:3 (2003), 765–791
J. Brüning, S. Yu. Dobrokhotov, M. A. Poteryakhin, “Integral Representation of Analytical Solutions of the Equation $yf_x'-xf_y'=g(x,y)$”, Mat. Zametki, 72:4 (2002), 633–634; Math. Notes, 72:4 (2002), 583–585
J. Brüning, S. Yu. Dobrokhotov, K. V. Pankrashin, “The Asymptotic Form of the Lower Landau Bands in a Strong Magnetic Field”, TMF, 131:2 (2002), 304–331; Theoret. and Math. Phys., 131:2 (2002), 704–728
J. Brüning, S. Yu. Dobrokhotov, M. A. Poteryakhin, “Averaging for Hamiltonian Systems with One Fast Phase and Small Amplitudes”, Mat. Zametki, 70:5 (2001), 660–669; Math. Notes, 70:5 (2001), 599–607
V. V. Belov, O. S. Dobrokhotov, S. Yu. Dobrokhotov, “Isotropic Tori, Complex Germ and Maslov Index, Normal Forms and Quasimodes of Multidimensional Spectral Problems”, Mat. Zametki, 69:4 (2001), 483–514; Math. Notes, 69:4 (2001), 437–466
S. Yu. Dobrokhotov, A. I. Shafarevich, “Tunnel Splitting of the Spectrum of the Beltrami–Laplace Operators on Two-Dimensional Surfaces with Square Integrable Geodesic Flow”, Funktsional. Anal. i Prilozhen., 34:2 (2000), 67–69; Funct. Anal. Appl., 34:2 (2000), 133–134
R. O. Hryniv, S. Yu. Dobrokhotov, A. A. Shkalikov, “An operator model for the oscillation problem of liquids on an elastic bottom”, Mat. Zametki, 68:1 (2000), 66–81; Math. Notes, 68:1 (2000), 57–70
S. Yu. Dobrokhotov, “Integrability of truncated Hugoniot–Maslov chains for trajectories of mesoscale vortices on shallow water”, TMF, 125:3 (2000), 491–518; Theoret. and Math. Phys., 125:3 (2000), 1724–1741
A. Boutet de Monvel, S. Yu. Dobrokhotov, “Random perturbations of invariant Lagrangian tori of Hamiltonian vector fields”, Mat. Zametki, 64:5 (1998), 783–787; Math. Notes, 64:5 (1998), 674–679
S. Yu. Dobrokhotov, “Integrability by quadratures of Hamiltonian $2n$-dimensional systems with $n$ known skew-orthogonal solutions”, Uspekhi Mat. Nauk, 53:2(320) (1998), 143–144; Russian Math. Surveys, 53:2 (1998), 380–381
S. Yu. Dobrokhotov, “Hugoniot–Maslov chains for trajectories of point vortex singularities of shallow water equations, and the Hill equation”, Dokl. Akad. Nauk, 354:5 (1997), 600–603
S. Yu. Dobrokhotov, “Reduction of Hugoniot–Maslov chains for trajectories of solitary vortices of the “shallow water” equations to the Hill equation”, TMF, 112:1 (1997), 47–66; Theoret. and Math. Phys., 112:1 (1997), 827–843
S. Yu. Dobrokhotov, V. Martìnez Olivè, “Lissajous figures, two-dimensional tori, and the spectral series of a three-dimensional anharmonic oscillator”, Algebra i Analiz, 8:2 (1996), 121–128; St. Petersburg Math. J., 8:2 (1997), 273–279
94.
S. Yu. Dobrokhotov, “On the reduction to Hill's equation of a Hugoniot–Maslov chain for trajectories of pointwise singularities of shallow water equation”, Uspekhi Mat. Nauk, 51:6(312) (1996), 203–204; Russian Math. Surveys, 51:6 (1996), 1195–1197
S. Yu. Dobrokhotov, O. L. Tolstova, “Asymptotic eigenfunctions and generalized eigenfunctions of an operator related to wave motions of a fluid over an elastic slightly nonflat bottom”, Mat. Zametki, 58:6 (1995), 917–922; Math. Notes, 58:6 (1995), 1336–1340
96.
S. Yu. Dobrokhotov, V. N. Kolokoltsov, V. Martines Olive, “Asymptotically stable invariant tori of a vector field $V(x)$ and the quasimodes of the operator $V(x)\cdot\nabla-\varepsilon\Delta$”, Mat. Zametki, 58:2 (1995), 301–306; Math. Notes, 58:2 (1995), 880–884
V. V. Bulatov, Yu. V. Vladimirov, V. G. Danilov, S. Yu. Dobrokhotov, “An example of the computation of the “eye” of a hurricane based
on a conjecture of V. P. Maslov”, Dokl. Akad. Nauk, 338:1 (1994), 102–105
V. V. Belov, S. Yu. Dobrokhotov, V. Martines Olive, “Some quasiclassical spectral series in a quantum anisotropic
Kepler problem”, Dokl. Akad. Nauk, 331:2 (1993), 150–154; Dokl. Math., 38:7 (1993), 263–266
S. Yu. Dobrokhotov, O. L. Tolstova, I. Yu. Chudinovich, “Waves in a fluid over an elastic bottom. The existence theorem and exact solutions”, Mat. Zametki, 54:6 (1993), 33–55; Math. Notes, 54:6 (1993), 1208–1222
S. Yu. Dobrokhotov, V. Martines Olive, “Localized asymptotic solutions of the magneto dynamo equation in $ABC$ fields”, Mat. Zametki, 54:4 (1993), 45–68; Math. Notes, 54:4 (1993), 1010–1025
S. Yu. Dobrokhotov, P. N. Zhevandrov, V. M. Kuzmina, “Asymptotics of the solution of the Cauchy–Poisson problem in a layer of nonconstant thickness”, Mat. Zametki, 53:6 (1993), 141–145; Math. Notes, 53:6 (1993), 657–660
S. Yu. Dobrokhotov, V. N. Kolokoltsov, “Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential”, TMF, 94:3 (1993), 426–434; Theoret. and Math. Phys., 94:3 (1993), 300–305
S. Yu. Dobrokhotov, V. P. Maslov, V. B. Tsvetkov, “Problem of the reversal of a wave for the model equation $r_t+rr_X-\dfrac{ih}{2}r_{XX}=0$”, Mat. Zametki, 51:6 (1992), 143–147; Math. Notes, 51:6 (1992), 624–627
S. Yu. Dobrokhotov, A. I. Shafarevich, “Parametrix and the asymptotics of localized solutions of the Navier-Stokes equations in $\mathbf{R}^3$, linearized on a smooth flow”, Mat. Zametki, 51:1 (1992), 72–82; Math. Notes, 51:1 (1992), 47–54
V. V. Belov, S. Yu. Dobrokhotov, “Semiclassical maslov asymptotics with complex phases. I. General approach”, TMF, 92:2 (1992), 215–254; Theoret. and Math. Phys., 92:2 (1992), 843–868
S. Yu. Dobrokhotov, I. M. Krichever, “Multi-phase solutions of the Benjamin–Ono equation and their averaging”, Mat. Zametki, 49:6 (1991), 42–58; Math. Notes, 49:6 (1991), 583–594
S. Yu. Dobrokhotov, P. N. Zhevandrov, V. P. Maslov, A. I. Shafarevich, “Asymptotic fast-decreasing solutions of linear, strictly hyperbolic systems with variable coefficients”, Mat. Zametki, 49:4 (1991), 31–46; Math. Notes, 49:4 (1991), 355–365
S. Yu. Dobrokhotov, V. N. Kolokoltsov, V. P. Maslov, “Splitting of the lowest energy levels of the Schrödinger equation and asymptotic behavior of the fundamental solution of the equation $hu_t=h^2\Delta u/2-V(x)u$”, TMF, 87:3 (1991), 323–375; Theoret. and Math. Phys., 87:3 (1991), 561–599
S. Yu. Dobrokhotov, O. L. Tolstova, “Application of conservation laws in asymptotic problems for equations with an operator-valued symbol”, Mat. Zametki, 47:5 (1990), 148–151
Yu. M. Vorob'ev, S. Yu. Dobrokhotov, “Basis systems on the torus generated by finite-zone integration of the Korteweg–de Vries equation”, Mat. Zametki, 47:1 (1990), 47–61; Math. Notes, 47:1 (1990), 32–41
1989
112.
S. Yu. Dobrokhotov, M. B. Konovalov, I. Kh. Kostin, “Localization of Green function and the application of transition functions in problems of seismic wave effect on large structures”, Dokl. Akad. Nauk SSSR, 304:5 (1989), 1101–1105
1988
113.
V. V. Belov, S. Yu. Dobrokhotov, “The Maslov canonical operator on isotropic manifolds with a
complex germ, and its applications to spectral problems”, Dokl. Akad. Nauk SSSR, 298:5 (1988), 1037–1042; Dokl. Math., 37:1 (1988), 180–185
Yu. M. Vorob'ev, S. Yu. Dobrokhotov, “Completeness of the system of eigenfunctions of a nonelliptic operator on the torus, generated by a Hill operator with a finite-zone potential”, Funktsional. Anal. i Prilozhen., 22:2 (1988), 65–66; Funct. Anal. Appl., 22:2 (1988), 137–139
S. Yu. Dobrokhotov, “Resonance correction to an adiabatically perturbed finite-zonal almost periodic solution of the Korteweg–de Vries equation”, Mat. Zametki, 44:4 (1988), 551–555
S. Yu. Dobrokhotov, “Resonances in asymptotic solutions of the Cauchy problem for the Schrödinger equation with rapidly oscillating finite-zone potential”, Mat. Zametki, 44:3 (1988), 319–340; Math. Notes, 44:3 (1988), 656–668
L. V. Berlyand, S. Yu. Dobrokhotov, ““Operator separation of variables” in problems of short-wave
asymptotics for differential equations with rapidly oscillating
coefficients”, Dokl. Akad. Nauk SSSR, 296:1 (1987), 80–84
S. Yu. Dobrokhotov, A. I. Shafarevich, “Quasiclassical asymptotics in the problem of the scattering of
wave packets by a rapidly changing potential of the form $-2\vert
\nabla\Phi\vert ^2/{\rm ch}^2(\Phi (x)/h)+V_0(x)$”, Dokl. Akad. Nauk SSSR, 295:6 (1987), 1347–1351
119.
S. Yu. Dobrokhotov, “Nonlocal analogues of the nonlinear Boussinesq equation for surface waves over an uneven bottom and their asymptotic solutions”, Dokl. Akad. Nauk SSSR, 292:1 (1987), 63–67
1986
120.
S. Yu. Dobrokhotov, “Asymptotics of surface waves captured by shores and by
inhomogeneities in the bottom relief”, Dokl. Akad. Nauk SSSR, 289:3 (1986), 575–579
S. Yu. Dobrokhotov, P. N. Zhevandrov, “Nonstandard characteristics and Maslov's operatorial method in linear problems concerning unsteady water waves”, Funktsional. Anal. i Prilozhen., 19:4 (1985), 43–54; Funct. Anal. Appl., 19:4 (1985), 285–295
B. Valigno, S. Yu. Dobrokhotov, N. N. Nekhoroshev, “The complex germ in systems with one cyclic variable”, Uspekhi Mat. Nauk, 39:3(237) (1984), 233–234; Russian Math. Surveys, 39:3 (1984), 219–220
Yu. M. Vorob'ev, S. Yu. Dobrokhotov, V. P. Maslov, “Quasiclassical approximation for the models of spin-spin interaction on the one-dimensional lattice”, Zap. Nauchn. Sem. LOMI, 133 (1984), 63–76
1983
124.
S. Yu. Dobrokhotov, “Maslov's methods in the linearized theory of gravitational waves on a fluid surface”, Dokl. Akad. Nauk SSSR, 269:1 (1983), 76–80
S. Yu. Dobrokhotov, V. P. Maslov, “Multidimensional Dirichlet series in the problem of the asymptotic behavior of spectral series of nonlinear elliptic operators”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 23 (1983), 137–222; J. Soviet Math., 28:1 (1985), 91–143
Yu. M. Vorob'ev, S. Yu. Dobrokhotov, “Quasiclassical asymptotic behaviors for discrete models of electron-phonon interaction: Maslov's method and the adiabatic approximation”, TMF, 57:1 (1983), 63–74; Theoret. and Math. Phys., 57:1 (1983), 993–1001
Yu. M. Vorob'ev, S. Yu. Dobrokhotov, “Quasiclassical quantization of the periodic Toda chain from the point of view of Lie algebras”, TMF, 54:3 (1983), 477–480; Theoret. and Math. Phys., 54:3 (1983), 312–314
S. Yu. Dobrokhotov, V. P. Maslov, “Finite-zone almost periodic solutions in WKB-approximations”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 15 (1980), 3–94; J. Soviet Math., 16:6 (1981), 1433–1487
S. Yu. Dobrokhotov, V. P. Maslov, “Problem of reflection from a boundary for the equation $h^2\square u+à\operatorname{sh}u=0$ and finite-zone conditionally periodic solutions”, Funktsional. Anal. i Prilozhen., 13:3 (1979), 79–80; Funct. Anal. Appl., 13:3 (1979), 220–222
S. Yu. Dobrokhotov, V. P. Maslov, “Resonance fenomena in the nonlinear equation of a proper semiconductor $h^2\Delta u=\operatorname{sh}u$”, Zap. Nauchn. Sem. LOMI, 84 (1979), 35–44; J. Soviet Math., 21:3 (1983), 274–280
S. Yu. Dobrokhotov, V. P. Maslov, “Asymptotics of a spectral boundary-value problem for a nonlinear equation for semiconductors”, Dokl. Akad. Nauk SSSR, 243:4 (1978), 897–900
S. Yu. Dobrokhotov, V. P. Maslov, “Certain applications of the theory of a complex germ to equations with a small parameter”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 5 (1975), 141–211; J. Soviet Math., 5:4 (1976), 552–605
S. O. Gorchinskiy, V. G. Danilov, S. Yu. Dobrokhotov, V. V. Kozlov, V. E. Nazaikinskii, N. N. Nefedov, D. O. Orlov, S. A. Stepin, I. A. Taimanov, D. V. Treschev, N. A. Tyurin, A. T. Fomenko, S. E. Yakush, “Andrei Igorevich Shafarevich (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 79:3(477) (2024), 185–188; Russian Math. Surveys, 79:3 (2024), 553–556
2021
134.
V. M. Buchstaber, A. N. Varchenko, A. P. Veselov, P. G. Grinevich, S. Grushevsky, S. Yu. Dobrokhotov, A. V. Zabrodin, A. V. Marshakov, A. E. Mironov, N. A. Nekrasov, S. P. Novikov, A. Yu. Okounkov, M. A. Olshanetsky, A. K. Pogrebkov, I. A. Taimanov, M. A. Tsfasman, L. O. Chekhov, O. K. Sheinman, S. B. Shlosman, “Igor' Moiseevich Krichever (on his 70th birthday)”, Uspekhi Mat. Nauk, 76:4(460) (2021), 183–193; Russian Math. Surveys, 76:4 (2021), 733–743
M. I. Belishev, S. Yu. Dobrokhotov, I. A. Ibragimov, A. P. Kiselev, S. V. Kislyakov, M. A. Lyalinov, Yu. V. Matiyasevich, V. G. Romanov, V. P. Smyshlyaev, T. A. Suslina, N. N. Ural'tseva, “Vasilii Mikhailovich Babich (on his ninetieth birthday)”, Uspekhi Mat. Nauk, 76:1(457) (2021), 201–202; Russian Math. Surveys, 76:1 (2021), 193–194
A. V. Artem'ev, S. V. Bolotin, D. L. Vainchtein, A. A. Vasiliev, S. Yu. Dobrokhotov, L. M. Zelenyi, V. V. Kozlov, A. A. Petrukovich, V. V. Sidorenko, D. V. Treschev, A. I. Shafarevich, “Anatolii Iserovish Neishtadt (on his 70th birthday)”, Uspekhi Mat. Nauk, 75:5(455) (2020), 201–208; Russian Math. Surveys, 75:5 (2020), 981–989
2015
137.
V. V. Grushin, S. Yu. Dobrokhotov, S. A. Sergeev, “Correction to the paper “Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source” (Proc. Steklov Inst. Math. 281, 161–178 (2013))”, Trudy Mat. Inst. Steklova, 288 (2015
