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Dobrokhotov Sergey Yur'evich

Publications in Math-Net.Ru

  1. 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
  2. Averaging method for problems on quasiclassical asymptotics

    CMFD, 70:1 (2024),  53–76
  3. On the arguments of Jacobians in local expressions of the Maslov canonical operator

    Mat. Zametki, 116:6 (2024),  1264–1276
  4. 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
  5. Classical and Wave Dynamics of Long Nonlinear Waves Localized in the Vicinity of Gently Sloping Shores

    Trudy Mat. Inst. Steklova, 327 (2024),  27–43
  6. 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
  7. 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
  8. 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
  9. Lagrangian manifolds and the construction of asymptotics for (pseudo)differential equations with localized right-hand sides

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

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

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

    TMF, 213:1 (2022),  163–190
  13. 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
  14. 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
  15. Representations of Bessel functions via the Maslov canonical operator

    TMF, 208:2 (2021),  196–217
  16. 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
  17. Lagrangian Manifolds and Efficient Short-Wave Asymptotics in a Neighborhood of a Caustic Cusp

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

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

    TMF, 204:2 (2020),  171–180
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. Classical and Quantum Dynamics of a Particle in a Narrow Angle

    Regul. Chaotic Dyn., 24:6 (2019),  704–716
  26. 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
  27. 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
  28. 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
  29. 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
  30. Exact Step-Like Solutions of One-Dimensional Shallow-Water Equations over a Sloping Bottom

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

    Mat. Zametki, 104:6 (2018),  835–850
  32. 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
  33. One Approach to the Computation of Asymptotics of Integrals of Rapidly Varying Functions

    Mat. Zametki, 103:5 (2018),  680–692
  34. 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
  35. Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber

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

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

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

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

    Mat. Zametki, 101:6 (2017),  936–943
  40. 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
  41. Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics

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

    Mat. Zametki, 100:6 (2016),  855–867
  43. 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
  44. 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
  45. 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
  46. 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
  47. 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
  48. 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
  49. Homogenization in the Problem of Long Water Waves over a Bottom Site with Fast Oscillations

    Mat. Zametki, 95:3 (2014),  359–375
  50. 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
  51. Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms

    TMF, 178:3 (2014),  322–345
  52. 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
  53. Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source

    Trudy Mat. Inst. Steklova, 281 (2013),  170–187
  54. 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
  55. 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
  56. Averaging of Linear Operators, Adiabatic Approximation, and Pseudodifferential Operators

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    Mat. Zametki, 69:4 (2001),  483–514
  81. 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
  82. An operator model for the oscillation problem of liquids on an elastic bottom

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

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

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

    Uspekhi Mat. Nauk, 53:2(320) (1998),  143–144
  86. 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
  87. 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
  88. Lissajous figures, two-dimensional tori, and the spectral series of a three-dimensional anharmonic oscillator

    Algebra i Analiz, 8:2 (1996),  121–128
  89. 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
  90. 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
  91. 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
  92. 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
  93. Some quasiclassical spectral series in a quantum anisotropic Kepler problem

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

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

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

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

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

    TMF, 94:3 (1993),  426–434
  99. 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
  100. 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
  101. Semiclassical maslov asymptotics with complex phases. I. General approach

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

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

    Mat. Zametki, 49:4 (1991),  31–46
  104. 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
  105. Application of conservation laws in asymptotic problems for equations with an operator-valued symbol

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

    Mat. Zametki, 47:1 (1990),  47–61
  107. 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
  108. 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
  109. 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
  110. Resonance correction to an adiabatically perturbed finite-zonal almost periodic solution of the Korteweg–de Vries equation

    Mat. Zametki, 44:4 (1988),  551–555
  111. 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
  112. “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
  113. 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
  114. 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
  115. Asymptotics of surface waves captured by shores and by inhomogeneities in the bottom relief

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

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

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

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

    Dokl. Akad. Nauk SSSR, 269:1 (1983),  76–80
  120. 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
  121. Quasiclassical asymptotic behaviors for discrete models of electron-phonon interaction: Maslov's method and the adiabatic approximation

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

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

    Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 15 (1980),  3–94
  124. 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
  125. 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
  126. Asymptotics of a spectral boundary-value problem for a nonlinear equation for semiconductors

    Dokl. Akad. Nauk SSSR, 243:4 (1978),  897–900
  127. 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

  128. Andrei Igorevich Shafarevich (on his sixtieth birthday)

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

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

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

    Uspekhi Mat. Nauk, 75:5(455) (2020),  201–208
  132. 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
  133. Igor Krichever

    Mosc. Math. J., 10:4 (2010),  833–834
  134. 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
  135. Fiftieth anniversary of research and teaching by Viktor Pavlovich Maslov

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

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

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

    Uspekhi Mat. Nauk, 51:1(307) (1996),  133–136
  139. 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
  140. Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics

    Uspekhi Mat. Nauk, 34:3(207) (1979),  221–226
  141. 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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