# zbMATH — the first resource for mathematics

## Dobrokhotov, Sergei Yurievich

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 Author ID: dobrokhotov.sergei-yu Published as: Dobrochotov, S. Yu.; Dobrohotov, S. Ju.; Dobrokhotov, S.; Dobrokhotov, S. Y.; Dobrokhotov, S. Yu; Dobrokhotov, S. Yu.; Dobrokhotov, Sergei; Dobrokhotov, Sergei Yu.; Dobrokhotov, Sergeiĭ Yu.; Dobrokhotov, Sergej Yu.; Dobrokhotov, Sergey; Dobrokhotov, Serguej Yu. Homepage: http://www.ipmnet.ru/~dobr/ External Links: Math-Net.Ru · ORCID
 Documents Indexed: 211 Publications since 1975
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#### Co-Authors

 12 single-authored 34 Nazaikinskii, Vladimir E. 32 Tirozzi, Brunello 24 Maslov, Viktor Pavlovich 24 Shafarevich, Andreĭ Igorevich 23 Brüning, Jochen 12 Anikin, A. Yu. 12 Minenkov, Dmitrii S. 11 Tudorovskii, T. Ya. 10 Belov, Vladimir Vasilyevich 8 Grushin, V. V. 8 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 8 Semenov, E. S. 7 Pankrashkin, Konstantin 7 Tolchennikov, Anton A. 7 Zhevandrov, Peter N. 6 Kolokoltsov, Vassili N. 6 Olivé, Victor M. 6 Sergeev, Sergeĭ Alekseevich 6 Tsvetkova, Anna V. 5 Albeverio, Sergio A. 5 Nekrasov, R. V. 5 Tolstova, O. L. 4 Danilov, Vladimir G. 4 Poteryakhin, M. A. 4 Rouleux, Michel 4 Vorob’ev, Yu. M. 3 Bulatov, Vitaly V. 3 Katsnelson, Mikhail I. 3 Klevin, A. I. 3 Kuz’mina, V. M. 3 Makrakis, George N. 3 Maksimov, V. A. 3 Vargas, Carlos A. 3 Vladimirov, Yu. V. 2 Anikin, Anatoly Y. 2 Chebotarev, Alexandr M. 2 Chernous’ko, Feliks Leonidovich 2 Logunov, Anatoliĭ Alekseevich 2 Lozhnikov, D. A. 2 Martínez-Olivé, Victor 2 Medvedev, Sergeĭ Borisovich 2 Nekhoroshev, Nikolaĭ Nikolaevich 2 Pavlov, Boris Sergeevich 2 Petrov, P. N. 2 Semënov, Evgeniĭ Mikhaĭlovich 2 Shlosman, Semen B. 2 Sinitsyn, S. O. 2 Sturova, Izolda V. 2 Vorobjev, Yurii M. 1 Aksenov, Alexander V. 1 Allilueva, Anna I. 1 Araf’eva, I. Ya. 1 Babich, Vasiliĭ Mikhaĭlovich 1 Berlyand, Leonid V. 1 Bianchi, Daniela 1 Boutet de Monvel, Anne Marie 1 Buldyrev, V. S. 1 Bykov, Dmitri V. 1 Cardinali, Alessandro 1 Chirkunov, Yuriĭ Aleksandrovich 1 Chudinovich, Igor Yuryevich 1 Dobrokhotov, O. S. 1 Druzhkov, K. P. 1 Escamilla Reyna, Juan Alberto 1 Exner, Pavel 1 Fradkin, L. Yu. 1 Frost, V. A. 1 Gershtein, S. S. 1 Geyler, Vladimir A. 1 Griniv, R. O. 1 Kholevo, Aleksandr Semënovich 1 Kaloshin, V. A. 1 Karasev, Mikhail Vladimirovich 1 Kazakov, Dmitri I. 1 Klimenko, M. V. 1 Klimov, Dmitrij M. 1 Korobkin, Alexander A. 1 Koshmanenko, Volodymyr Dmytrovych 1 Krichever, Igor’ Moiseevich 1 Kryukovskij, A. S. 1 Kucherenko, Valeri V. 1 Kulish, Petr Petrovich 1 Libanov, M. V. 1 Lukin, Dmitry S. 1 Lyalinov, Mikhail Anatolievich 1 Marshakov, Andrei V. 1 Martines Olive, Victor 1 Martinez-Olive, W. 1 Mendoza Torres, Francisco Javier 1 Molotkov, I. A. 1 Morozov, Alexei Yurievich 1 Neishtadt, Anatoly I. 1 Nosikov, I. A. 1 Olive, V. Martines 1 Omel’yanov, Georgii A. 1 Osipov, Yuriĭ Sergeevich 1 Plakida, N. M. 1 Popov, A. L. 1 Popov, Alexander V. 1 Popov, Igor’ Yur’evich ...and 18 more Co-Authors
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#### Serials

 45 Russian Journal of Mathematical Physics 41 Mathematical Notes 27 Theoretical and Mathematical Physics 12 Doklady Mathematics 6 Doklady Akademii Nauk 5 Journal of Soviet Mathematics 5 Soviet Physics. Doklady 4 Russian Mathematical Surveys 4 Functional Analysis and its Applications 3 Matematicheskie Zametki 3 Computational Mathematics and Mathematical Physics 3 Regular and Chaotic Dynamics 3 Proceedings of the Steklov Institute of Mathematics 2 Journal of Engineering Mathematics 2 Funktsional’nyĭ Analiz i ego Prilozheniya 2 Asymptotic Analysis 2 Journal of Mathematical Sciences (New York) 2 St. Petersburg Mathematical Journal 1 Fluid Dynamics 1 Geophysical and Astrophysical Fluid Dynamics 1 Journal of Applied Mathematics and Mechanics 1 Journal of Mathematical Physics 1 Soviet Scientific Reviews. Section C 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Prikladnaya Matematika i Mekhanika 1 Theory of Probability and its Applications 1 Soviet Mathematics. Doklady 1 Transactions of the Moscow Mathematical Society 1 Algebra i Analiz 1 Annals of Physics 1 Physics-Doklady 1 Izvestiya: Mathematics 1 Mathematical Physics, Analysis and Geometry 1 Differential Equations 1 Journal of Mathematical Physics, Analysis, Geometry 1 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 1 Mathematical Modelling of Natural Phenomena
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#### Fields

 135 Partial differential equations (35-XX) 67 Fluid mechanics (76-XX) 55 Quantum theory (81-XX) 31 Dynamical systems and ergodic theory (37-XX) 19 Ordinary differential equations (34-XX) 19 Geophysics (86-XX) 15 Differential geometry (53-XX) 12 Mechanics of particles and systems (70-XX) 11 Statistical mechanics, structure of matter (82-XX) 10 Operator theory (47-XX) 8 Global analysis, analysis on manifolds (58-XX) 5 History and biography (01-XX) 5 Mechanics of deformable solids (74-XX) 4 Special functions (33-XX) 4 Optics, electromagnetic theory (78-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 General and overarching topics; collections (00-XX) 2 Probability theory and stochastic processes (60-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH

141 Publications have been cited 794 times in 302 Documents Cited by Year
Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations. Zbl 1180.35336
Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B.
2008
Operator separation of variables for adiabatic problems in quantum and wave mechanics. Zbl 1110.81080
Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskiy, T. Ya.
2006
Representations of rapidly decaying functions by the Maslov canonical operator. Zbl 1344.58014
Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I.
2007
Asymptotic fast-decreasing solutions of linear, strictly hyperbolic systems with variable coefficients. Zbl 0735.35089
Dobrokhotov, S. Yu.; Zhevandrov, P. N.; Maslov, V. P.; Shafarevich, A. I.
1991
New formulas for Maslov’s canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics. Zbl 1298.81091
Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E.; Tudorovskii, T. Ya.
2013
Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I. Zbl 1387.35404
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2010
Asymptotic expansions and the Maslov canonical opeator in the linear theory of water waves. I: Main constructions and equations for surface gravity waves. Zbl 1065.76026
Dobrokhotov, S. Yu.; Zhevandrov, P. N.
2003
Maslov’s methods in the linearized theory of gravitational waves on a fluid surface. Zbl 0533.76013
Dobrokhotov, S. Yu.
1983
Finite-zone, almost-periodic solutions in WKB approximations. Zbl 0461.35010
Dobrokhotov, S. Yu.; Maslov, V. P.
1981
Punctured Lagrangian manifolds and asymptotic solutions of the linear water wave equations with localized initial conditions. Zbl 06769034
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2017
Asymptotic solutions of the linear shallow-water equations with localized initial data. Zbl 1325.76036
Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tirozzi, B.
2011
Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations. Zbl 1178.35301
Dobrokhotov, S. Yu.; Tirozzi, B.; Vargas, C. A.
2009
Finite-zone almost periodic solutions in WKB-approximations. Zbl 0446.35008
Dobrokhotov, S. Yu.; Maslov, V. P.
1980
Some integral identities and remarks on the decay at infinity of the solutions to the Navier-Stokes equations in the entire space. Zbl 0976.35508
Dobrokhotov, Sergej Yu.; Shafarevich, Andrej I.
1994
Multiphase asymptotics of nonlinear partial differential equations with a small parameter. Zbl 0551.35072
Dobrokhotov, S. Yu.; Maslov, V. P.
1982
Asymptotic solutions of nonrelativistic equations of quantum mechanics in curved nanotubes. I: Reduction to spatially one-dimensional equations. Zbl 1178.81080
Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya.
2004
Multi-phase solutions of the Benjamin-Ono equation and their averaging. Zbl 0752.35058
Dobrokhotov, S. Yu.; Krichever, I. M.
1991
New representations of the Maslov canonical operator and localized asymptotic solutions for strictly hyperbolic systems. Zbl 1331.35219
Allilueva, A. I.; Dobrokhotov, S. Yu.; Sergeev, S. A.; Shafarevich, A. I.
2015
Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data. Zbl 1320.35180
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2013
The spectral asymptotics of the two-dimensional Schrödinger operator with a strong magnetic field. I. Zbl 1104.81046
Brüning, J.; Dobrokhotov, S. Yu.; Pankrashkin, K. V.
2002
Description of tsunami propagation based on the Maslov canonical operator. Zbl 1152.35089
Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskii, T. Ya.
2006
Splitting of the lowest energy levels of the Schrödinger equation and asymptotic behavior of the fundamental solution of the equation $$hu_ t=h^ 2\Delta u/2-V(x)u$$. Zbl 0745.35033
Dobrokhotov, S. Yu.; Kolokol’tsov, V. N.; Maslov, V. P.
1991
Asymptotic solutions of the Cauchy problem with localized initial conditions for linearized two-dimensional Boussinesq-type equations with variable coefficients. Zbl 1276.76012
Dobrokhotov, S. Yu.; Sergeev, S. A.; Tirozzi, B.
2013
Localized solutions of one-dimensional non-linear shallow-water equations with velocity $$c=\sqrt x$$. Zbl 1196.35161
Dobrokhotov, S. Yu; Tirozzi, B.
2010
Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I: The Cauchy problem. Zbl 1146.35055
Dobrokhotov, S. Yu.; Sinitsyn, S. O.; Tirozzi, B.
2007
Quantum and classical dynamics of an electron in thin curved tubes with spin and external electromagnetic fields taken into account. Zbl 1186.81061
Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya.
2004
Nonstandard characteristics and Maslov’s operational method in linear problems concerning unsteady water waves. Zbl 0625.35080
Dobrokhotov, S. Yu.; Zhevandrov, P. N.
1985
New integral representations of the Maslov canonical operator in singular charts. Zbl 1369.81033
Dobrokhotov, Sergei Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I.
2017
Unstable closed trajectories, librations and splitting of the lowest eigenvalues in quantum double well problem. Zbl 1164.81312
Brüning, J.; Dobrokhotov, S. Yu.; Semenov, E. S.
2006
“Momentum” tunneling between tori and the splitting of eigenvalues of the Laplace-Beltrami operator on Liouville surfaces. Zbl 0968.58025
Dobrokhotov, S. Yu.; Shafarevich, A. I.
1999
Characteristics with singularities and the boundary values of the asymptotic solution of the Cauchy problem for a degenerate wave equation. Zbl 1362.35170
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2016
A class of exact algebraic localized solutions of the multidimensional wave equation. Zbl 1234.35142
Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya.
2010
The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory. Zbl 1200.53072
Dobrokhotov, S. Yu.; Rouleux, M.
2010
Description of a tsunami wave propagation on the ground of the Maslov canonical operator. Zbl 1119.76311
Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskij, T. Ya.
2006
Averaging for Hamiltonian systems with one fast phase and small amplitudes. Zbl 1025.37038
Brüning, Jochen; Dobrokhotov, S. Yu.; Poteryakhin, M. A.
2001
On the behavior of an incompressible fluid velocity field at infinity. Zbl 0889.76011
Dobrokhotov, S. Yu.; Shafarevich, A. I.
1996
Asymptotic solutions of linearized Navier-Stokes equations. Zbl 0816.76025
Dobrokhotov, S. Yu.; Shafarevich, A. I.
1993
Exact and asymptotic solutions of the Cauchy-Poisson problem with localized initial conditions and a constant function of the bottom. Zbl 1386.76082
Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya.; Tolchennikov, A. A.
2017
Averaging of linear operators, adiabatic approximation, and pseudodifferential operators. Zbl 1282.47079
Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.
2012
The semi-classical Maupertuis-Jacobi correspondence for quasi-periodic Hamiltonian flows with applications to linear water waves theory. Zbl 1242.37042
Dobrokhotov, Sergey; Rouleux, Michel
2011
Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential. Zbl 0799.35050
Dobrokhotov, S. Yu.; Kolokol’tsov, V. N.
1993
Parametrix and asymptotics of localized solutions of Navier-Stokes equations in $$R^ 3$$ linearized on a smooth flow. Zbl 0751.76020
Dobrokhotov, S. Yu.; Shafarevich, A. I.
1992
Maslov’s canonical operator, Hörmander’s formula, and localization of the Berry-Balazs solution in the theory of wave beams. Zbl 1323.81031
Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E.
2014
Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source. Zbl 1293.35279
Grushin, V. V.; Dobrokhotov, S. Yu.; Sergeev, S. A.
2013
Asymptotic solutions of the Schrödinger equation in thin tubes. Zbl 1126.35354
Belov, V. V.; Dobrokhotov, S. Yu.; Sinitsyn, S. O.
2003
Isotropic tori, complex germ and Maslov index, normal forms and quasimodes of multidimensional spectral problems. Zbl 1013.58014
Belov, V. V.; Dobrokhotov, O. S.; Dobrokhotov, S. Yu.
2001
Propagation of a linear wave created by a spatially localized perturbation in a regular lattice and punctured Lagrangian manifolds. Zbl 1376.37114
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2017
The Maupertuis-Jacobi principle for Hamiltonians of the form $$F(x,|p|)$$ in two-dimensional stationary semiclassical problems. Zbl 1360.37159
Dobrokhotov, S. Yu.; Minenkov, D. S.; Rouleux, M.
2015
Peierls substitution and the Maslov operator method. Zbl 1197.35086
Grushin, V. V.; Dobrokhotov, S. Yu.
2010
The spectral asymptotics of the two-dimensional Schrödinger operator with a strong magnetic field. II. Zbl 1104.81307
Brüning, J.; Dobrokhotov, S. Yu.; Pankrashkin, K. V.
2002
The double-well splitting of the low energy levels for the Schrödinger operator of discrete $$\varphi^ 4$$-models on tori. Zbl 0820.60097
Dobrokhotov, Sergei Yu.; Kolokol’tsov, Vassili N.
1995
Asymptotics of the solution of the Cauchy-Poisson problem in a layer of nonconstant thickness. Zbl 0810.35084
Dobrokhotov, S. Yu.; Zhevandrov, P. N.; Kuz’mina, V. M.
1993
“Operator separation of variables” in problems of short-wave asymptotic behavior for differential equations with fast oscillating coefficients. Zbl 0671.35013
Berlyand, L. V.; Dobrokhotov, S. Yu.
1987
Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber. Zbl 1411.81090
Dobrokhotov, S. Yu.; Minenkov, D. S.; Shlosman, S. B.
2018
Electronic optics in graphene in the semiclassical approximation. Zbl 1397.78009
Reijnders, K. J. A.; Minenkov, D. S.; Katsnelson, M. I.; Dobrokhotov, S. Yu.
2018
On the asymptotics of a Bessel-type integral having applications in wave run-up theory. Zbl 1384.42001
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2017
Asymptotics of linear water waves generated by a localized source near the focal points on the leading edge. Zbl 1432.76203
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A.
2017
Volume and entropy in abstract analytic number theory and thermodynamics. Zbl 1362.82025
Maslov, V. P.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2016
Asymptotics of shallow water equations on the sphere. Zbl 1311.76012
Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A.
2014
Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. Zbl 1263.35154
Dobrokhotov, Sergey; Minenkov, Dmitrii; Nazaikinskii, Vladimir; Tirozzi, Brunello
2013
Generalized Foldy-Wouthuysen transformation and pseudodifferential operators. Zbl 1274.81069
Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya.
2011
Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. II: Taking into account a source on the right-hand side and a weak dispersion. Zbl 1194.35054
Bianchi, D.; Dobrokhotov, S. Yu.; Tirozzi, B.
2008
Cauchy–Riemann conditions and localized asymptotic solutions of linearized equations of shallow water theory. Zbl 1100.76506
Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I.
2005
Hugoniot-Maslov chains for solitary vortices of the shallow water equations. I: Derivation of the chains for the case of variable Coriolis forces and reduction to the Hill equation. Zbl 1059.76506
Dobrokhotov, S. Yu.
1999
Magnetic field asymptotics in a well conducting fluid. Zbl 1181.76152
Dobrokhotov, Sergei; Olive, Victor M.; Ruzmaikin, Alexander; Shafarevich, Andrei
1996
Resonances in asymptotic solutions of the Cauchy problem for the Schrödinger equation with rapidly oscillating finite-zone potential. Zbl 0667.35058
Dobrokhotov, S. Yu.
1988
Simple asymptotics for a generalized wave equation with degenerating velocity and their applications in the linear long wave run-up problem. Zbl 1420.35151
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2018
The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides. Zbl 1377.35062
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Rouleux, M.
2017
Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections. Zbl 1359.76057
Dobrokhotov, S. Yu.; Grushin, V. V.; Sergeev, S. A.; Tirozzi, B.
2016
Maslov’s canonical operator in arbitrary coordinates on the Lagrangian manifold. Zbl 1345.53083
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Shafarevich, A. I.
2016
Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms. Zbl 1297.76027
Chirkunov, Yu. A.; Dobrokhotov, S. Yu.; Medvedev, S. B.; Minenkov, D. S.
2014
Splitting of lower energy levels in a quantum double well in a magnetic field and tunneling of wave packets in nanowires. Zbl 1286.81057
Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V.
2013
Asymptotics of waves on the shallow water generated by spatially-localized sources and trapped by underwater ridges. Zbl 1276.76011
Dobrokhotov, S. Yu.; Lozhnikov, D. A.; Vargas, C. A.
2013
Approximate formulas for eigenvalues of the Laplace operator on a torus arising in linear problems with oscillating coefficients. Zbl 1257.35135
Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.
2012
Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data. Zbl 1230.35057
Dobrokhotov, S. Yu.; Nazaĭkinskiĭ, V. E.; Tirozzi, B.
2011
Asymptotic solutions of 2D wave equations with variable velocity and localized right-hand side. Zbl 1192.35110
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2010
Quantum dynamics in a thin film. I: Propagation of localized perturbations. Zbl 1175.81117
Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tudorovskiy, T. Ya.
2008
Splitting formulas for the higher and lower energy levels of the one-dimensional Schrödinger operator. Zbl 1178.81070
Albeverio, S.; Dobrokhotov, S. Yu.; Semenov, E. S.
2004
Explicit formulas for generalized action-angle variables in a neighborhood of an isotropic torus and their application. Zbl 1178.37055
Belov, V. V.; Dobrokhotov, S. Yu.; Maksimov, V. A.
2003
Quantization of the Bellman equation, exponential asymptotics and tunneling. Zbl 0796.35141
Dobrokhotov, S. Yu.; Kolokoltsov, V. N.; Maslov, V. P.
1992
The short-wave asymptotics in a linearized system of equations of hydrodynamics with rapidly varying coefficients. Zbl 0850.35076
Dobrokhotov, S. Yu; Shafarevich, A. I.
1988
Lagrangian manifolds related to the asymptotics of Hermite polynomials. Zbl 1409.42019
Dobrokhotov, S. Yu.; Tsvetkova, A. V.
2018
Efficient formulas for the Maslov canonical operator near a simple caustic. Zbl 1406.81036
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2018
Waves on the free surface described by linearized equations of hydrodynamics with localized right-hand sides. Zbl 1388.76028
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2018
Uniform asymptotics of the boundary values of the solution in a linear problem on the run-up of waves on a shallow beach. Zbl 1372.35180
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A.
2017
Maslov complex germ and high-frequency Gaussian beams for cold plasma in a toroidal domain. Zbl 1354.82032
Dobrokhotov, S. Yu.; Cardinali, A.; Klevin, A. I.; Tirozzi, Brunello
2016
Simple exact and asymptotic solutions of the 1D run-up problem over a slowly varying (quasiplanar) bottom. Zbl 1329.35246
Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E.; Tirozzi, B.
2016
On a homogenization method for differential operators with oscillating coefficients. Zbl 1326.35022
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2015
Homogenization in the problem of long water waves over a bottom site with fast oscillations. Zbl 1315.35165
Grushin, V. V.; Dobrokhotov, S. Yu.
2014
On transforms reducing one-dimensional systems of shallow-water to the wave equation with sound speed $$c^2=x$$. Zbl 1307.76010
Dobrokhotov, S. Yu.; Medvedev, S. B.; Minenkov, D. S.
2013
Remark on the phase shift in the Kuzmak-Whitham ansatz. Zbl 1274.35356
Dobrokhotov, S. Yu.; Minenkov, D. S.
2011
Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity. Zbl 1145.81351
Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V.; Shafarevich, A. I.
2008
On normal forms in a neighborhood of two-dimensional resonance tori for a multidimensional anharmonic oscillator. Zbl 1083.34031
Dobrokhotov, S. Yu.; Poteryakhin, M. A.
2004
Hugoniót-Maslov chains for singular vortical solutions to quasilinear hyperbolic systems and typhoon trajectory. Zbl 1069.37049
Dobrokhotov, S.; Semenov, E.; Tirozzi, B.
2003
On the Hamiltonian property of truncated Hugoniot-Maslov chains for trajectories of mesoscale vortices. Zbl 1074.76530
Dobrokhotov, S. Yu.; Tirozzi, B.
2002
Hugoniot-Maslov chains for solitary vortices of the shallow water equations. II: The analysis of solutions of the truncated chain and an approximate description of possible trajectories of mesoscale vortices (typhoons). Zbl 1060.76533
Dobrokhotov, S. Yu.
1999
Calculations of hurricane trajectory on the basis of V. P. Maslov hypothesis. Zbl 0872.35086
Bulatov, V. V.; Vladimirov, Yu. V.; Danilov, V. G.; Dobrokhotov, S. Yu.
1994
On motion of the point algebraic singularity for two-dimensional nonlinear equations of hydrodynamics. Zbl 0829.35095
Bulatov, V. V.; Vladimirov, Yu. V.; Danilov, V. G.; Dobrokhotov, S. Yu.
1994
Localized asymptotic solutions of the magneto dynamo equation in abc fields. Zbl 0865.35102
Dobrokhotov, S. Yu.; Martinez-Olive, W.
1993
Resonance correction to an adiabatically perturbed finite-zonal almost periodic solution of the Korteweg-de Vries equation. Zbl 0667.35063
Dobrokhotov, S. Yu.
1988
Uniform formulas for the asymptotic solution of a linear pseudodifferential equation describing water waves generated by a localized source. Zbl 1448.35391
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A.
2020
Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems. Zbl 1441.81091
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V.
2019
Asymptotics, related to billiards with semi-rigid walls, of eigenfunctions of the $$\nabla D(x)\nabla$$ operator in dimension 2 and trapped coastal waves. Zbl 1426.37049
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V.
2019
Solution of the two-dimensional Dirac equation with a linear potential and a localized initial condition. Zbl 1417.81126
Dobrokhotov, S. Yu.; Tolchennikov, A. A.
2019
Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber. Zbl 1411.81090
Dobrokhotov, S. Yu.; Minenkov, D. S.; Shlosman, S. B.
2018
Electronic optics in graphene in the semiclassical approximation. Zbl 1397.78009
Reijnders, K. J. A.; Minenkov, D. S.; Katsnelson, M. I.; Dobrokhotov, S. Yu.
2018
Simple asymptotics for a generalized wave equation with degenerating velocity and their applications in the linear long wave run-up problem. Zbl 1420.35151
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2018
Lagrangian manifolds related to the asymptotics of Hermite polynomials. Zbl 1409.42019
Dobrokhotov, S. Yu.; Tsvetkova, A. V.
2018
Efficient formulas for the Maslov canonical operator near a simple caustic. Zbl 1406.81036
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2018
Waves on the free surface described by linearized equations of hydrodynamics with localized right-hand sides. Zbl 1388.76028
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2018
Exact step-like solutions of one-dimensional shallow-water equations over a sloping bottom. Zbl 1415.35226
Aksenov, A. V.; Dobrokhotov, S. Yu.; Druzhkov, K. P.
2018
Punctured Lagrangian manifolds and asymptotic solutions of the linear water wave equations with localized initial conditions. Zbl 06769034
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2017
New integral representations of the Maslov canonical operator in singular charts. Zbl 1369.81033
Dobrokhotov, Sergei Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I.
2017
Exact and asymptotic solutions of the Cauchy-Poisson problem with localized initial conditions and a constant function of the bottom. Zbl 1386.76082
Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya.; Tolchennikov, A. A.
2017
Propagation of a linear wave created by a spatially localized perturbation in a regular lattice and punctured Lagrangian manifolds. Zbl 1376.37114
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2017
On the asymptotics of a Bessel-type integral having applications in wave run-up theory. Zbl 1384.42001
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2017
Asymptotics of linear water waves generated by a localized source near the focal points on the leading edge. Zbl 1432.76203
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A.
2017
The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides. Zbl 1377.35062
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Rouleux, M.
2017
Uniform asymptotics of the boundary values of the solution in a linear problem on the run-up of waves on a shallow beach. Zbl 1372.35180
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A.
2017
Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics. Zbl 1393.82023
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Klevin, A. I.; Tirozzi, B.
2017
Averaging and trajectories of a Hamiltonian system appearing in graphene placed in a strong magnetic field and a periodic potential. Zbl 1394.82019
Anikin, A.; Brüning, J.; Dobrokhotov, S. Yu.
2017
Characteristics with singularities and the boundary values of the asymptotic solution of the Cauchy problem for a degenerate wave equation. Zbl 1362.35170
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2016
Volume and entropy in abstract analytic number theory and thermodynamics. Zbl 1362.82025
Maslov, V. P.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2016
Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections. Zbl 1359.76057
Dobrokhotov, S. Yu.; Grushin, V. V.; Sergeev, S. A.; Tirozzi, B.
2016
Maslov’s canonical operator in arbitrary coordinates on the Lagrangian manifold. Zbl 1345.53083
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Shafarevich, A. I.
2016
Maslov complex germ and high-frequency Gaussian beams for cold plasma in a toroidal domain. Zbl 1354.82032
Dobrokhotov, S. Yu.; Cardinali, A.; Klevin, A. I.; Tirozzi, Brunello
2016
Simple exact and asymptotic solutions of the 1D run-up problem over a slowly varying (quasiplanar) bottom. Zbl 1329.35246
Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E.; Tirozzi, B.
2016
Approximation of solutions of the two-dimensional wave equation with variable velocity and localized right-hand side using some “simple” solutions. Zbl 1362.35169
Dobrokhotov, S. Yu.; Anikin, A. Yu.
2016
Lower part of the spectrum for the two-dimensional Schrödinger operator periodic in one variable and application to quantum dimers. Zbl 1349.81096
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Katsnelson, M. I.
2016
Semiclassical asymptotic approximations and the density of states for the two-dimensional radially symmetric Schrödinger and Dirac equations in tunnel microscopy problems. Zbl 1338.81182
Brüning, J.; Dobrokhotov, S. Yu.; Katsnelson, M. I.; Minenkov, D. S.
2016
New representations of the Maslov canonical operator and localized asymptotic solutions for strictly hyperbolic systems. Zbl 1331.35219
Allilueva, A. I.; Dobrokhotov, S. Yu.; Sergeev, S. A.; Shafarevich, A. I.
2015
The Maupertuis-Jacobi principle for Hamiltonians of the form $$F(x,|p|)$$ in two-dimensional stationary semiclassical problems. Zbl 1360.37159
Dobrokhotov, S. Yu.; Minenkov, D. S.; Rouleux, M.
2015
On a homogenization method for differential operators with oscillating coefficients. Zbl 1326.35022
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2015
Maslov’s canonical operator, Hörmander’s formula, and localization of the Berry-Balazs solution in the theory of wave beams. Zbl 1323.81031
Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E.
2014
Asymptotics of shallow water equations on the sphere. Zbl 1311.76012
Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A.
2014
Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms. Zbl 1297.76027
Chirkunov, Yu. A.; Dobrokhotov, S. Yu.; Medvedev, S. B.; Minenkov, D. S.
2014
Homogenization in the problem of long water waves over a bottom site with fast oscillations. Zbl 1315.35165
Grushin, V. V.; Dobrokhotov, S. Yu.
2014
Fourier integrals and a new representation of Maslov’s canonical operator near caustics. Zbl 1320.81058
Dobrokhotov, S. Yu.; Makrakis, G.; Nazaikinskii, V. E.
2014
New formulas for Maslov’s canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics. Zbl 1298.81091
Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E.; Tudorovskii, T. Ya.
2013
Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data. Zbl 1320.35180
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2013
Asymptotic solutions of the Cauchy problem with localized initial conditions for linearized two-dimensional Boussinesq-type equations with variable coefficients. Zbl 1276.76012
Dobrokhotov, S. Yu.; Sergeev, S. A.; Tirozzi, B.
2013
Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source. Zbl 1293.35279
Grushin, V. V.; Dobrokhotov, S. Yu.; Sergeev, S. A.
2013
Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. Zbl 1263.35154
Dobrokhotov, Sergey; Minenkov, Dmitrii; Nazaikinskii, Vladimir; Tirozzi, Brunello
2013
Splitting of lower energy levels in a quantum double well in a magnetic field and tunneling of wave packets in nanowires. Zbl 1286.81057
Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V.
2013
Asymptotics of waves on the shallow water generated by spatially-localized sources and trapped by underwater ridges. Zbl 1276.76011
Dobrokhotov, S. Yu.; Lozhnikov, D. A.; Vargas, C. A.
2013
On transforms reducing one-dimensional systems of shallow-water to the wave equation with sound speed $$c^2=x$$. Zbl 1307.76010
Dobrokhotov, S. Yu.; Medvedev, S. B.; Minenkov, D. S.
2013
Averaging of linear operators, adiabatic approximation, and pseudodifferential operators. Zbl 1282.47079
Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.
2012
Approximate formulas for eigenvalues of the Laplace operator on a torus arising in linear problems with oscillating coefficients. Zbl 1257.35135
Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.
2012
Asymptotic solutions of the linear shallow-water equations with localized initial data. Zbl 1325.76036
Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tirozzi, B.
2011
The semi-classical Maupertuis-Jacobi correspondence for quasi-periodic Hamiltonian flows with applications to linear water waves theory. Zbl 1242.37042
Dobrokhotov, Sergey; Rouleux, Michel
2011
Generalized Foldy-Wouthuysen transformation and pseudodifferential operators. Zbl 1274.81069
Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya.
2011
Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data. Zbl 1230.35057
Dobrokhotov, S. Yu.; Nazaĭkinskiĭ, V. E.; Tirozzi, B.
2011
Remark on the phase shift in the Kuzmak-Whitham ansatz. Zbl 1274.35356
Dobrokhotov, S. Yu.; Minenkov, D. S.
2011
Spectral series of the Schrödinger operator in a thin waveguide with a periodic structure. II: Closed three-dimensional waveguide in a magnetic field. Zbl 1251.35099
Brüning, J.; Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya.; Tudorovskiy, T. Ya.
2011
Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I. Zbl 1387.35404
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2010
Localized solutions of one-dimensional non-linear shallow-water equations with velocity $$c=\sqrt x$$. Zbl 1196.35161
Dobrokhotov, S. Yu; Tirozzi, B.
2010
A class of exact algebraic localized solutions of the multidimensional wave equation. Zbl 1234.35142
Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya.
2010
The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory. Zbl 1200.53072
Dobrokhotov, S. Yu.; Rouleux, M.
2010
Peierls substitution and the Maslov operator method. Zbl 1197.35086
Grushin, V. V.; Dobrokhotov, S. Yu.
2010
Asymptotic solutions of 2D wave equations with variable velocity and localized right-hand side. Zbl 1192.35110
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2010
On various averaging methods for a nonlinear oscillator with slow time-dependent potential and a nonconservative perturbation. Zbl 1209.34050
Dobrokhotov, S. Yu.; Minenkov, D. S.
2010
Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations. Zbl 1178.35301
Dobrokhotov, S. Yu.; Tirozzi, B.; Vargas, C. A.
2009
Quantum dynamics in a thin film. II: Stationary states. Zbl 1182.81038
Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V.
2009
Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations. Zbl 1180.35336
Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B.
2008
Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. II: Taking into account a source on the right-hand side and a weak dispersion. Zbl 1194.35054
Bianchi, D.; Dobrokhotov, S. Yu.; Tirozzi, B.
2008
Quantum dynamics in a thin film. I: Propagation of localized perturbations. Zbl 1175.81117
Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tudorovskiy, T. Ya.
2008
Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity. Zbl 1145.81351
Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V.; Shafarevich, A. I.
2008
Representations of rapidly decaying functions by the Maslov canonical operator. Zbl 1344.58014
Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I.
2007
Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I: The Cauchy problem. Zbl 1146.35055
Dobrokhotov, S. Yu.; Sinitsyn, S. O.; Tirozzi, B.
2007
Operator separation of variables for adiabatic problems in quantum and wave mechanics. Zbl 1110.81080
Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskiy, T. Ya.
2006
Description of tsunami propagation based on the Maslov canonical operator. Zbl 1152.35089
Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskii, T. Ya.
2006
Unstable closed trajectories, librations and splitting of the lowest eigenvalues in quantum double well problem. Zbl 1164.81312
Brüning, J.; Dobrokhotov, S. Yu.; Semenov, E. S.
2006
Description of a tsunami wave propagation on the ground of the Maslov canonical operator. Zbl 1119.76311
Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskij, T. Ya.
2006
Spectral series of the Schrödinger operator in thin waveguides with periodic structure. I: Adiabatic approximation and semiclassical asymptotics in the 2D case. Zbl 1113.81031
Brüning, J.; Dobrokhotov, S.; Sekerzh-Zenkovich, S.; Tudorovskiy, T.
2006
Cauchy–Riemann conditions and localized asymptotic solutions of linearized equations of shallow water theory. Zbl 1100.76506
Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I.
2005
A perturbative theory of the evolution of the center of typhoons. Zbl 1169.86307
Dobrokhotov, Sergey; Semenov, Evgeny; Tirozzi, Brunello
2005
On the theory of multiple scattering of waves and the optical potential for a system of point-like scatterers. An application to the theory of ultracold neutrons. Zbl 1190.81136
Brüning, J.; Dobrokhotov, S. Yu.; Geyler, V. A.; Tudorovskiy, T. Ya.
2005
On quasimodes of small diffusion operators corresponding to stable invariant tori with nonregular neighborhoods. Zbl 1192.35040
Albeverio, Sergio; Dobrokhotov, Sergey; Poteryakhin, Michael
2005
Asymptotic solutions of nonrelativistic equations of quantum mechanics in curved nanotubes. I: Reduction to spatially one-dimensional equations. Zbl 1178.81080
Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya.
2004
Quantum and classical dynamics of an electron in thin curved tubes with spin and external electromagnetic fields taken into account. Zbl 1186.81061
Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya.
2004
Splitting formulas for the higher and lower energy levels of the one-dimensional Schrödinger operator. Zbl 1178.81070
Albeverio, S.; Dobrokhotov, S. Yu.; Semenov, E. S.
2004
On normal forms in a neighborhood of two-dimensional resonance tori for a multidimensional anharmonic oscillator. Zbl 1083.34031
Dobrokhotov, S. Yu.; Poteryakhin, M. A.
2004
Asymptotic expansions and the Maslov canonical opeator in the linear theory of water waves. I: Main constructions and equations for surface gravity waves. Zbl 1065.76026
Dobrokhotov, S. Yu.; Zhevandrov, P. N.
2003
Asymptotic solutions of the Schrödinger equation in thin tubes. Zbl 1126.35354
Belov, V. V.; Dobrokhotov, S. Yu.; Sinitsyn, S. O.
2003
Explicit formulas for generalized action-angle variables in a neighborhood of an isotropic torus and their application. Zbl 1178.37055
Belov, V. V.; Dobrokhotov, S. Yu.; Maksimov, V. A.
2003
Hugoniót-Maslov chains for singular vortical solutions to quasilinear hyperbolic systems and typhoon trajectory. Zbl 1069.37049
Dobrokhotov, S.; Semenov, E.; Tirozzi, B.
2003
The spectral asymptotics of the two-dimensional Schrödinger operator with a strong magnetic field. I. Zbl 1104.81046
Brüning, J.; Dobrokhotov, S. Yu.; Pankrashkin, K. V.
2002
The spectral asymptotics of the two-dimensional Schrödinger operator with a strong magnetic field. II. Zbl 1104.81307
Brüning, J.; Dobrokhotov, S. Yu.; Pankrashkin, K. V.
2002
On the Hamiltonian property of truncated Hugoniot-Maslov chains for trajectories of mesoscale vortices. Zbl 1074.76530
Dobrokhotov, S. Yu.; Tirozzi, B.
2002
The asymptotic form of the lower Landau bands in a strong magnetic field. Zbl 1039.81023
Brüning, J.; Dobrokhotov, S. Yu.; Pankrashkin, K. V.
2002
Integral representation of analytical solutions of the equation $$yf_x'-xf_y'=g(x,y)$$. Zbl 1130.35318
Brüning, J.; Dobrokhotov, S. Yu.; Poteryakhin, M. A.
2002
Averaging for Hamiltonian systems with one fast phase and small amplitudes. Zbl 1025.37038
Brüning, Jochen; Dobrokhotov, S. Yu.; Poteryakhin, M. A.
2001
Isotropic tori, complex germ and Maslov index, normal forms and quasimodes of multidimensional spectral problems. Zbl 1013.58014
Belov, V. V.; Dobrokhotov, O. S.; Dobrokhotov, S. Yu.
2001
On Maslov’s conjecture on the structure of weak point singularities of the shallow water equations. Zbl 1090.76513
Dobrokhotov, S. Yu.; Pankrashkin, K. V.; Semenov, E. S.
2001
An operator model for the oscillation problem of liquids on an elastic bottom. Zbl 0973.35140
Griniv, R. O.; Dobrokhotov, S. Yu.; Shkalikov, A. A.
2000
Tunnel splitting of the spectrum of the Beltrami-Laplace operators on two-dimensional surfaces with square integrable geodesic flow. Zbl 1019.58009
Dobrokhotov, S. Yu.; Shafarevich, A. I.
2000
“Momentum” tunneling between tori and the splitting of eigenvalues of the Laplace-Beltrami operator on Liouville surfaces. Zbl 0968.58025
Dobrokhotov, S. Yu.; Shafarevich, A. I.
1999
Hugoniot-Maslov chains for solitary vortices of the shallow water equations. I: Derivation of the chains for the case of variable Coriolis forces and reduction to the Hill equation. Zbl 1059.76506
Dobrokhotov, S. Yu.
1999
Hugoniot-Maslov chains for solitary vortices of the shallow water equations. II: The analysis of solutions of the truncated chain and an approximate description of possible trajectories of mesoscale vortices (typhoons). Zbl 1060.76533
Dobrokhotov, S. Yu.
1999
Integrability by quadratures of Hamiltonian $$2n$$-dimensional systems with $$n$$ known skew-orthogonal solutions. Zbl 0929.70014
Dobrokhotov, S. Yu.
1998
...and 41 more Documents
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#### Cited by 228 Authors

 86 Dobrokhotov, Sergei Yurievich 34 Shafarevich, Andreĭ Igorevich 33 Nazaikinskii, Vladimir E. 19 Tirozzi, Brunello 15 Anikin, A. Yu. 15 Maslov, Viktor Pavlovich 14 Grushin, V. V. 13 Tolchennikov, Anton A. 12 Allilueva, Anna I. 12 Brüning, Jochen 12 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 12 Sergeev, Sergeĭ Alekseevich 9 Minenkov, Dmitrii S. 7 Tsvetkova, Anna V. 7 Vybornyi, E. V. 5 Helffer, Bernard 5 Karasev, Mikhail Vladimirovich 5 Kucherenko, Valeri V. 5 Miller, Peter D. 5 Rabinovich, Vladimir Samuilovich 5 Tudorovskii, T. Ya. 4 Belov, Vladimir Vasilyevich 4 Bulatov, Vitaly V. 4 Klevin, A. I. 4 Lozhnikov, D. A. 4 Mal’tsev, Andreĭ Yakovlevich 4 Nekrasov, R. V. 4 Novikova, E. M. 4 Vladimirov, Yu. V. 4 Zhevandrov, Peter N. 3 Aida, Shigeki 3 Kaljakin, Leonid A. 3 Kalyakin, Leonid Anatol’evich 3 Kordyukov, Yuri A. 3 Kryvko, Andriy 3 Kuksin, Sergeĭ B. 3 Kulikovskiĭ, Andreĭ Gennad’evich 3 Vargas, Carlos A. 3 Volkov, B. I. 3 Vorobjev, Yurii M. 2 Babich, Vasiliĭ Mikhaĭlovich 2 Bikbaev, Ramil’ F. 2 Borisov, Denis Ivanovich 2 Brandolese, Lorenzo 2 Chang, Tongkeun 2 Chirkunov, Yuriĭ Aleksandrovich 2 Dell’Antonio, Gian Fausto 2 Dubrovin, Boris Anatol’evich 2 El, Gennady A. 2 Gelfreich, Vasily G. 2 Haberman, Richard 2 Hu, Chinkun 2 Jin, Bum Ja 2 Kabanikhin, Sergeĭ Igorevich 2 Katsnelson, Mikhail I. 2 Konishi, Eiji 2 Krichever, Igor’ Moiseevich 2 Krivorotko, Olga I. 2 Kukavica, Igor 2 Lerman, Lev 2 Makrakis, George N. 2 Maksimov, V. A. 2 Medvedev, Sergeĭ Borisovich 2 Moll, Alexander C. 2 Neishtadt, Anatoly I. 2 Pankrashkin, Konstantin 2 Perel, Maria V. 2 Pereskokov, A. V. 2 Petrov, P. N. 2 Petrov, P. S. 2 Qin, Yuming 2 Rouleux, Michel 2 Rozanova, Olga S. 2 Smyth, Noel F. 2 Tolstova, O. L. 2 Topalov, Peter J. 2 Vladimirov, I. Yu. 2 Wetzel, Alfredo N. 2 Yu, Jui-Ling 2 Zhang, Jianlin 1 Abenda, Simonetta 1 Abramian, Andrei K. 1 Agafonov, Sergey I. 1 Aksenov, Alexander V. 1 Albeverio, Sergio A. 1 Ambrose, David M. 1 Anikin, Anatoly Y. 1 Azhotkin, V. D. 1 Baev, Andrey V. 1 Bestuzheva, Alla Nikolaevna 1 Bianchi, Daniela 1 Bihlo, Alexander 1 Bourland, F. Jay 1 Brezhnev, Yurii V. 1 Burlak, Gennadiy 1 Caputo, Pietro 1 Cardinali, Alessandro 1 Cardone, Giuseppe 1 Chebotarev, Alexandr M. 1 Chernyshev, Vsevolod L. ...and 128 more Authors
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#### Cited in 62 Serials

 68 Russian Journal of Mathematical Physics 60 Mathematical Notes 30 Theoretical and Mathematical Physics 11 Journal of Mathematical Physics 10 Doklady Mathematics 8 Physica D 8 Proceedings of the Steklov Institute of Mathematics 7 Journal of Applied Mathematics and Mechanics 7 Journal of Soviet Mathematics 5 Functional Analysis and its Applications 5 Journal of Mathematical Sciences (New York) 4 Fluid Dynamics 4 Prikladnaya Matematika i Mekhanika 4 Journal of Functional Analysis 4 Computational Mathematics and Mathematical Physics 4 Regular and Chaotic Dynamics 3 Journal of Differential Equations 2 International Journal of Modern Physics A 2 Applicable Analysis 2 Communications in Mathematical Physics 2 Journal of Engineering Mathematics 2 Journal of Fluid Mechanics 2 Mathematical Methods in the Applied Sciences 2 Russian Mathematical Surveys 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Studies in Applied Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Differential Equations 2 Nonlinear Analysis. Real World Applications 1 Communications on Pure and Applied Mathematics 1 Geophysical and Astrophysical Fluid Dynamics 1 International Journal of Theoretical Physics 1 Reports on Mathematical Physics 1 Reviews in Mathematical Physics 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Journal of the London Mathematical Society. Second Series 1 Memoirs of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 Transactions of the American Mathematical Society 1 Revista Matemática Iberoamericana 1 Forum Mathematicum 1 Geometric and Functional Analysis. GAFA 1 SIAM Journal on Mathematical Analysis 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Journal of Nonlinear Science 1 Nuclear Physics, B, Proceedings Supplements 1 St. Petersburg Mathematical Journal 1 Izvestiya: Mathematics 1 Chaos 1 European Journal of Mechanics. B. Fluids 1 Russian Physics Journal 1 Matematicheskoe Modelirovanie 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Communications in Mathematical Analysis 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Pseudo-Differential Operators and Applications 1 Ufimskiĭ Matematicheskiĭ Zhurnal 1 Mathematics 1 Nonlinear Analysis. Theory, Methods & Applications
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#### Cited in 36 Fields

 192 Partial differential equations (35-XX) 107 Fluid mechanics (76-XX) 72 Quantum theory (81-XX) 37 Dynamical systems and ergodic theory (37-XX) 22 Ordinary differential equations (34-XX) 21 Operator theory (47-XX) 20 Statistical mechanics, structure of matter (82-XX) 19 Geophysics (86-XX) 16 Differential geometry (53-XX) 14 Optics, electromagnetic theory (78-XX) 11 Global analysis, analysis on manifolds (58-XX) 11 Mechanics of particles and systems (70-XX) 6 Numerical analysis (65-XX) 6 Mechanics of deformable solids (74-XX) 4 Special functions (33-XX) 3 Algebraic geometry (14-XX) 3 Topological groups, Lie groups (22-XX) 3 Difference and functional equations (39-XX) 3 Probability theory and stochastic processes (60-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Astronomy and astrophysics (85-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)