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Dobrokhotov Sergey Yur'evich

Publications in Math-Net.Ru

  1. Averaging method for problems on quasiclassical asymptotics

    CMFD, 70:1 (2024),  53–76
  2. 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
  3. 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
  4. 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
  5. 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
  6. Lagrangian manifolds and the construction of asymptotics for (pseudo)differential equations with localized right-hand sides

    TMF, 214:1 (2023),  3–29
  7. Plancherel–Rotach type asymptotic formulae for multiple orthogonal Hermite polynomials and recurrence relations

    Izv. RAN. Ser. Mat., 86:1 (2022),  36–97
  8. On Expansions in the Exact and Asymptotic Eigenfunctions of the One-Dimensional Schrödinger Operator

    Mat. Zametki, 112:5 (2022),  644–664
  9. Librations with large periods in tunneling: Efficient calculation and applications to trigonal dimers

    TMF, 213:1 (2022),  163–190
  10. 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
  11. 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
  12. Representations of Bessel functions via the Maslov canonical operator

    TMF, 208:2 (2021),  196–217
  13. 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
  14. Lagrangian Manifolds and Efficient Short-Wave Asymptotics in a Neighborhood of a Caustic Cusp

    Mat. Zametki, 108:3 (2020),  334–359
  15. Uniformization of Equations with Bessel-Type Boundary Degeneration and Semiclassical Asymptotics

    Mat. Zametki, 107:5 (2020),  780–786
  16. Airy function and transition between the semiclassical and harmonic oscillator approximations for one-dimensional bound states

    TMF, 204:2 (2020),  171–180
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. Classical and Quantum Dynamics of a Particle in a Narrow Angle

    Regul. Chaotic Dyn., 24:6 (2019),  704–716
  23. 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
  24. 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
  25. 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
  26. 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
  27. Exact Step-Like Solutions of One-Dimensional Shallow-Water Equations over a Sloping Bottom

    Mat. Zametki, 104:6 (2018),  930–936
  28. Lagrangian Manifolds Related to the Asymptotics of Hermite Polynomials

    Mat. Zametki, 104:6 (2018),  835–850
  29. 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
  30. One Approach to the Computation of Asymptotics of Integrals of Rapidly Varying Functions

    Mat. Zametki, 103:5 (2018),  680–692
  31. 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
  32. Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber

    TMF, 197:2 (2018),  269–278
  33. Gausian packets and beams with focal points in vector problems of plasma physics

    TMF, 196:1 (2018),  135–160
  34. New integral representations of the Maslov canonical operator in singular charts

    Izv. RAN. Ser. Mat., 81:2 (2017),  53–96
  35. On the Asymptotics of a Bessel-Type Integral Having Applications in Wave Run-Up Theory

    Mat. Zametki, 102:6 (2017),  828–835
  36. Punctured Lagrangian manifolds and asymptotic solutions of linear water wave equations with localized initial conditions

    Mat. Zametki, 101:6 (2017),  936–943
  37. 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
  38. Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics

    TMF, 193:3 (2017),  409–433
  39. Volume and Entropy in Abstract Analytic Number Theory and Thermodynamics

    Mat. Zametki, 100:6 (2016),  855–867
  40. 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
  41. 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
  42. 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
  43. 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
  44. 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
  45. 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
  46. Homogenization in the Problem of Long Water Waves over a Bottom Site with Fast Oscillations

    Mat. Zametki, 95:3 (2014),  359–375
  47. 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
  48. Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms

    TMF, 178:3 (2014),  322–345
  49. 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
  50. Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source

    Trudy Mat. Inst. Steklova, 281 (2013),  170–187
  51. 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
  52. 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
  53. Averaging of Linear Operators, Adiabatic Approximation, and Pseudodifferential Operators

    Mat. Zametki, 92:2 (2012),  163–180
  54. Generalized Foldy–Wouthuysen transformation and pseudodifferential operators

    TMF, 167:2 (2011),  171–192
  55. Remark on the phase shift in the Kuzmak–Whitham ansatz

    TMF, 166:3 (2011),  350–365
  56. Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data

    Algebra i Analiz, 22:6 (2010),  67–90
  57. A Class of Exact Algebraic Localized Solutions of the Multidimensional Wave Equation

    Mat. Zametki, 88:6 (2010),  942–945
  58. Peierls Substitution and the Maslov Operator Method

    Mat. Zametki, 87:4 (2010),  554–571
  59. The Semiclassical Maupertuis–Jacobi Correspondence and Applications to Linear Water Waves Theory

    Mat. Zametki, 87:3 (2010),  458–463
  60. Localized solutions of one-dimensional non-linear shallow-water equations with velocity $c=\sqrt x$

    Uspekhi Mat. Nauk, 65:1(391) (2010),  185–186
  61. Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity

    TMF, 155:2 (2008),  215–235
  62. Representations of Rapidly Decreasing Functions by the Maslov Canonical Operator

    Mat. Zametki, 82:5 (2007),  792–796
  63. Unstable closed trajectories, librations and splitting of the lowest eigenvalues in quantum double well problem

    Regul. Chaotic Dyn., 11:2 (2006),  167–180
  64. Non-Self-Adjointness of Operators with Small Diffusion

    Mat. Zametki, 78:6 (2005),  941–942
  65. Hugoniot–Maslov Chains for the System of Shallow-Water Equations Taking into Account Energy Exchange

    Mat. Zametki, 78:5 (2005),  796–799
  66. A generalized adiabatic principle for electron dynamics in curved nanostructures

    UFN, 175:9 (2005),  1004–1010
  67. Normal Forms near Two-Dimensional Resonance Tori for the Multidimensional Anharmonic Oscillator

    Mat. Zametki, 76:5 (2004),  701–713
  68. Asymptotic Solutions of Nonrelativistic Equations of Quantum Mechanics in Curved Nanotubes: I. Reduction to Spatially One-Dimensional Equations

    TMF, 141:2 (2004),  267–303
  69. Calculation of Integrals of the Hugoniot–Maslov Chain for Singular Vortical Solutions of the Shallow-Water Equation

    TMF, 139:1 (2004),  62–76
  70. Hugoniót–Maslov Chains for Singular Vortical Solutions to Quasilinear Hyperbolic Systems and Typhoon Trajectory

    CMFD, 2 (2003),  5–44
  71. Hall conductivity of minibands lying at the wings of Landau levels

    Pis'ma v Zh. Èksper. Teoret. Fiz., 77:11 (2003),  743–746
  72. Asymptotic solutions of the Schrödinger equation in thin tubes

    Trudy Inst. Mat. i Mekh. UrO RAN, 9:1 (2003),  15–25
  73. Explicit Formulas for Generalized Action–Angle Variables in a Neighborhood of an Isotropic Torus and Their Application

    TMF, 135:3 (2003),  378–408
  74. Integral Representation of Analytical Solutions of the Equation $yf_x'-xf_y'=g(x,y)$

    Mat. Zametki, 72:4 (2002),  633–634
  75. The Asymptotic Form of the Lower Landau Bands in a Strong Magnetic Field

    TMF, 131:2 (2002),  304–331
  76. Averaging for Hamiltonian Systems with One Fast Phase and Small Amplitudes

    Mat. Zametki, 70:5 (2001),  660–669
  77. Isotropic Tori, Complex Germ and Maslov Index, Normal Forms and Quasimodes of Multidimensional Spectral Problems

    Mat. Zametki, 69:4 (2001),  483–514
  78. 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
  79. An operator model for the oscillation problem of liquids on an elastic bottom

    Mat. Zametki, 68:1 (2000),  66–81
  80. Integrability of truncated Hugoniot–Maslov chains for trajectories of mesoscale vortices on shallow water

    TMF, 125:3 (2000),  491–518
  81. Random perturbations of invariant Lagrangian tori of Hamiltonian vector fields

    Mat. Zametki, 64:5 (1998),  783–787
  82. Integrability by quadratures of Hamiltonian $2n$-dimensional systems with $n$ known skew-orthogonal solutions

    Uspekhi Mat. Nauk, 53:2(320) (1998),  143–144
  83. 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
  84. 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
  85. Lissajous figures, two-dimensional tori, and the spectral series of a three-dimensional anharmonic oscillator

    Algebra i Analiz, 8:2 (1996),  121–128
  86. 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
  87. 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
  88. 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
  89. 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
  90. Some quasiclassical spectral series in a quantum anisotropic Kepler problem

    Dokl. Akad. Nauk, 331:2 (1993),  150–154
  91. Waves in a fluid over an elastic bottom. The existence theorem and exact solutions

    Mat. Zametki, 54:6 (1993),  33–55
  92. Localized asymptotic solutions of the magneto dynamo equation in $ABC$ fields

    Mat. Zametki, 54:4 (1993),  45–68
  93. Asymptotics of the solution of the Cauchy–Poisson problem in a layer of nonconstant thickness

    Mat. Zametki, 53:6 (1993),  141–145
  94. Some asymptotic solutions of linearized Navier–Stokes equations

    Mat. Zametki, 53:1 (1993),  25–35
  95. Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential

    TMF, 94:3 (1993),  426–434
  96. 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
  97. 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
  98. Semiclassical maslov asymptotics with complex phases. I. General approach

    TMF, 92:2 (1992),  215–254
  99. Multi-phase solutions of the Benjamin–Ono equation and their averaging

    Mat. Zametki, 49:6 (1991),  42–58
  100. Asymptotic fast-decreasing solutions of linear, strictly hyperbolic systems with variable coefficients

    Mat. Zametki, 49:4 (1991),  31–46
  101. 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
  102. Application of conservation laws in asymptotic problems for equations with an operator-valued symbol

    Mat. Zametki, 47:5 (1990),  148–151
  103. Basis systems on the torus generated by finite-zone integration of the Korteweg–de Vries equation

    Mat. Zametki, 47:1 (1990),  47–61
  104. 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
  105. 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
  106. 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
  107. Resonance correction to an adiabatically perturbed finite-zonal almost periodic solution of the Korteweg–de Vries equation

    Mat. Zametki, 44:4 (1988),  551–555
  108. 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
  109. “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
  110. 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
  111. 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
  112. Asymptotics of surface waves captured by shores and by inhomogeneities in the bottom relief

    Dokl. Akad. Nauk SSSR, 289:3 (1986),  575–579
  113. Nonstandard characteristics and Maslov's operatorial method in linear problems concerning unsteady water waves

    Funktsional. Anal. i Prilozhen., 19:4 (1985),  43–54
  114. The complex germ in systems with one cyclic variable

    Uspekhi Mat. Nauk, 39:3(237) (1984),  233–234
  115. Quasiclassical approximation for the models of spin-spin interaction on the one-dimensional lattice

    Zap. Nauchn. Sem. LOMI, 133 (1984),  63–76
  116. Maslov's methods in the linearized theory of gravitational waves on a fluid surface

    Dokl. Akad. Nauk SSSR, 269:1 (1983),  76–80
  117. 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
  118. Quasiclassical asymptotic behaviors for discrete models of electron-phonon interaction: Maslov's method and the adiabatic approximation

    TMF, 57:1 (1983),  63–74
  119. Quasiclassical quantization of the periodic Toda chain from the point of view of Lie algebras

    TMF, 54:3 (1983),  477–480
  120. Finite-zone almost periodic solutions in WKB-approximations

    Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 15 (1980),  3–94
  121. 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
  122. 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
  123. Asymptotics of a spectral boundary-value problem for a nonlinear equation for semiconductors

    Dokl. Akad. Nauk SSSR, 243:4 (1978),  897–900
  124. 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

  125. Andrei Igorevich Shafarevich (on his sixtieth birthday)

    Uspekhi Mat. Nauk, 79:3(477) (2024),  185–188
  126. Igor' Moiseevich Krichever (on his 70th birthday)

    Uspekhi Mat. Nauk, 76:4(460) (2021),  183–193
  127. Vasilii Mikhailovich Babich (on his ninetieth birthday)

    Uspekhi Mat. Nauk, 76:1(457) (2021),  201–202
  128. Anatolii Iserovish Neishtadt (on his 70th birthday)

    Uspekhi Mat. Nauk, 75:5(455) (2020),  201–208
  129. 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),  287
  130. Igor Krichever

    Mosc. Math. J., 10:4 (2010),  833–834
  131. On various averaging methods for a nonlinear oscillator with slow time-dependent potential and a nonconservative perturbation

    Regul. Chaotic Dyn., 15:2-3 (2010),  285–299
  132. Fiftieth anniversary of research and teaching by Viktor Pavlovich Maslov

    TMF, 155:2 (2008),  197–201
  133. Splitting Formulas for the Higher and Lower Energy Levels of the One-Dimensional Schrödinger Operator [Erratum]

    TMF, 141:3 (2004),  485
  134. Arlen Mikhailovich Il'in (A tribute in honor of his 70th birthday)

    Differ. Uravn., 38:8 (2002),  1011–1016
  135. Ramil' Faritovich Bikbaev (obituary)

    Uspekhi Mat. Nauk, 51:1(307) (1996),  133–136
  136. Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics (September, 30 – December, 9, 1987)

    Uspekhi Mat. Nauk, 43:3(261) (1988),  239–245
  137. Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics

    Uspekhi Mat. Nauk, 34:3(207) (1979),  221–226
  138. Sessions of the I. G. Petrovskii Seminar on Differential Equations and Mathematical Problems of Physics

    Uspekhi Mat. Nauk, 30:6(186) (1975),  197–206

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