Edit Profile (opens in new tab) Dobrokhotov, Sergei Yurievich Compute Distance To: Compute Author ID: dobrokhotov.sergei-yu Published as: Dobrokhotov, S. Yu.; Dobrokhotov, Sergei Yu.; Dobrokhotov, Sergey; Dobrokhotov, S.; Dobrokhotov, Sergey Yu.; Dobrokhotov, Sergei; Dobrohotov, S. Ju.; Dobrokhotov, S. Yu; Dobrokhotov, Sergeiĭ Yu.; Dobrokhotov, Serguej Yu.; Dobrokhotov, Sergej Yu.; Dobrochotov, S. Yu.; Dobrokhotov, S. Y. more...less Homepage: http://www.ipmnet.ru/~dobr/ External Links: ORCID · Google Scholar · Math-Net.Ru Documents Indexed: 226 Publications since 1975 1 Contribution as Editor Co-Authors: 152 Co-Authors with 213 Joint Publications 3,779 Co-Co-Authors all top 5 Co-Authors 12 single-authored 41 Nazaikinskii, Vladimir E. 32 Tirozzi, Brunello 26 Shafarevich, Andreĭ Igorevich 24 Maslov, Viktor Pavlovich 23 Brüning, Jochen 14 Anikin, A. Yu. 14 Minenkov, Dmitrii S. 11 Tudorovskii, T. Ya. 10 Belov, Vladimir Vasilyevich 10 Tsvetkova, Anna V. 8 Grushin, V. V. 8 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 8 Semenov, E. S. 7 Pankrashkin, Konstantin 7 Sergeev, Sergeĭ Alekseevich 7 Tolchennikov, Anton A. 7 Zhevandrov, Peter N. 6 Kolokoltsov, Vassili N. 6 Tolstova, O. L. 6 Vorob’ev, Yu. M. 5 Albeverio, Sergio A. 5 Nekrasov, R. V. 4 Danilov, V. G. 4 Olivé, Victor M. 4 Poteryakhin, M. A. 4 Rouleux, Michel 3 Bulatov, Vitaliĭ Vasil’evich 3 Katsnelson, Mikhail I. 3 Klevin, A. I. 3 Kuz’mina, V. M. 3 Makrakis, George N. 3 Maksimov, V. A. 3 Shlosman, Senya B. 3 Vargas, Carlos A. 2 Chebotarev, Alexandr M. 2 Chernous’ko, Feliks Leonidovich 2 Logunov, Anatoliĭ Alekseevich 2 Lozhnikov, D. A. 2 Lyalinov, Mikhail Anatolievich 2 Marshakov, Andrei V. 2 Martínez-Olivé, Victor 2 Medvedev, Sergeĭ Borisovich 2 Nekhoroshev, Nikolaĭ Nikolaevich 2 Pavlov, Boris Sergeevich 2 Petrov, P. N. 2 Shkalikov, Andreĭ Andreevich 2 Sinitsyn, S. O. 2 Sturova, Izolda V. 1 Allilueva, Anna I. 1 Anikin, Anatoly Y. 1 Aptekarev, Alexander Ivanovich 1 Araf’eva, I. Ya. 1 Artem’ev, A. V. 1 Babich, Vasiliĭ Mikhaĭlovich 1 Belishev, Mikhail Igorevitch 1 Berlyand, Leonid V. 1 Bianchi, Daniela 1 Bolotin, Sergeĭ Vladimirovich 1 Boutet de Monvel, Anne Marie 1 Bukhshtaber, Viktor Matveevich 1 Buldyrev, V. S. 1 Bykov, Dmitri V. 1 Cardinali, Alessandro 1 Chekhov, Leonid O. 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 Grinevich, Pëtr Georgievich 1 Griniv, R. O. 1 Grushevsky, S. M. 1 Kholevo, Aleksandr Semënovich 1 Ibragimov, Il’dar Abdullovich 1 Il’yasov, Kh. Kh. 1 Kaloshin, V. A. 1 Karasev, Mikhail Vladimirovich 1 Kazakov, Dmitri I. 1 Kislyakov, Sergeĭ Vital’evich 1 Klimenko, M. V. 1 Klimov, Dmitrij M. 1 Korobkin, Alexander A. 1 Koshmanenko, Volodymyr Dmytrovych 1 Kozlov, Valeriĭ Vasil’evich 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 Martines Olive, Victor 1 Martinez-Olive, W. 1 Matiyasevich, Yuriĭ Vladimirovich 1 Mendoza Torres, Francisco Javier 1 Mironov, Andreĭ Evgen’evich ...and 52 more Co-Authors all top 5 Serials 50 Russian Journal of Mathematical Physics 42 Mathematical Notes 28 Theoretical and Mathematical Physics 12 Doklady Mathematics 8 Russian Mathematical Surveys 6 Doklady Akademii Nauk 5 Journal of Soviet Mathematics 5 Soviet Physics. Doklady 4 Functional Analysis and its Applications 3 Matematicheskie Zametki 3 Computational Mathematics and Mathematical Physics 3 St. Petersburg Mathematical Journal 3 Regular and Chaotic Dynamics 3 Proceedings of the Steklov Institute of Mathematics 2 Fluid Dynamics 2 Journal of Engineering Mathematics 2 Funktsional’nyĭ Analiz i ego Prilozheniya 2 Asymptotic Analysis 2 Journal of Mathematical Sciences (New York) 2 Izvestiya: Mathematics 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 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 all top 5 Fields 143 Partial differential equations (35-XX) 69 Fluid mechanics (76-XX) 60 Quantum theory (81-XX) 30 Dynamical systems and ergodic theory (37-XX) 20 Ordinary differential equations (34-XX) 20 Geophysics (86-XX) 18 Differential geometry (53-XX) 12 Mechanics of particles and systems (70-XX) 11 Operator theory (47-XX) 11 Statistical mechanics, structure of matter (82-XX) 8 History and biography (01-XX) 8 Special functions (33-XX) 8 Global analysis, analysis on manifolds (58-XX) 6 Mechanics of deformable solids (74-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Optics, electromagnetic theory (78-XX) 3 Difference and functional equations (39-XX) 2 General and overarching topics; collections (00-XX) 2 Approximations and expansions (41-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 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 159 Publications have been cited 988 times in 362 Documents Cited by ▼ Year ▼ Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations. Zbl 1180.35336Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B. 46 2008 Operator separation of variables for adiabatic problems in quantum and wave mechanics. Zbl 1110.81080Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskiy, T. Ya. 32 2006 Representations of rapidly decaying functions by the Maslov canonical operator. Zbl 1344.58014Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 28 2007 Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I. Zbl 1387.35404Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 26 2010 Asymptotic fast-decreasing solutions of linear, strictly hyperbolic systems with variable coefficients. Zbl 0735.35089Dobrokhotov, S. Yu.; Zhevandrov, P. N.; Maslov, V. P.; Shafarevich, A. I. 24 1991 New formulas for Maslov’s canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics. Zbl 1298.81091Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E.; Tudorovskii, T. Ya. 22 2013 Punctured Lagrangian manifolds and asymptotic solutions of the linear water wave equations with localized initial conditions. Zbl 06769034Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 20 2017 Maslov’s methods in the linearized theory of gravitational waves on a fluid surface. Zbl 0533.76013Dobrokhotov, S. Yu. 19 1983 Asymptotic expansions and the Maslov canonical opeator in the linear theory of water waves. I: Main constructions and equations for surface gravity waves. Zbl 1065.76026Dobrokhotov, S. Yu.; Zhevandrov, P. N. 19 2003 New integral representations of the Maslov canonical operator in singular charts. Zbl 1369.81033Dobrokhotov, Sergei Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I. 19 2017 Some integral identities and remarks on the decay at infinity of the solutions to the Navier-Stokes equations in the entire space. Zbl 0976.35508Dobrokhotov, Sergej Yu.; Shafarevich, Andrej I. 18 1994 Finite-zone, almost-periodic solutions in WKB approximations. Zbl 0461.35010Dobrokhotov, S. Yu.; Maslov, V. P. 18 1981 Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations. Zbl 1178.35301Dobrokhotov, S. Yu.; Tirozzi, B.; Vargas, C. A. 17 2009 Asymptotic solutions of the linear shallow-water equations with localized initial data. Zbl 1325.76036Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tirozzi, B. 17 2011 Multi-phase solutions of the Benjamin-Ono equation and their averaging. Zbl 0752.35058Dobrokhotov, S. Yu.; Krichever, I. M. 17 1991 Finite-zone almost periodic solutions in WKB-approximations. (Endlichzonige fastperiodische Lösungen in WKB-Approximationen.) Zbl 0446.35008Dobrokhotov, S. Yu.; Maslov, V. P. 16 1980 Multiphase asymptotics of nonlinear partial differential equations with a small parameter. Zbl 0551.35072Dobrokhotov, S. Yu.; Maslov, V. P. 15 1982 Asymptotic solutions of nonrelativistic equations of quantum mechanics in curved nanotubes. I: Reduction to spatially one-dimensional equations. Zbl 1178.81080Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya. 15 2004 Localized solutions of one-dimensional non-linear shallow-water equations with velocity \(c=\sqrt x\). Zbl 1196.35161Dobrokhotov, S. Yu; Tirozzi, B. 14 2010 Description of tsunami propagation based on the Maslov canonical operator. Zbl 1152.35089Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskii, T. Ya. 13 2006 Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data. Zbl 1320.35180Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 13 2013 New representations of the Maslov canonical operator and localized asymptotic solutions for strictly hyperbolic systems. Zbl 1331.35219Allilueva, A. I.; Dobrokhotov, S. Yu.; Sergeev, S. A.; Shafarevich, A. I. 13 2015 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 0745.35033Dobrokhotov, S. Yu.; Kolokol’tsov, V. N.; Maslov, V. P. 13 1991 Asymptotic solutions of the Cauchy problem with localized initial conditions for linearized two-dimensional Boussinesq-type equations with variable coefficients. Zbl 1276.76012Dobrokhotov, S. Yu.; Sergeev, S. A.; Tirozzi, B. 12 2013 The spectral asymptotics of the two-dimensional Schrödinger operator with a strong magnetic field. I. Zbl 1104.81046Brüning, J.; Dobrokhotov, S. Yu.; Pankrashkin, K. V. 12 2002 Averaging for Hamiltonian systems with one fast phase and small amplitudes. Zbl 1025.37038Brüning, Jochen; Dobrokhotov, S. Yu.; Poteryakhin, M. A. 11 2001 Nonstandard characteristics and Maslov’s operational method in linear problems concerning unsteady water waves. Zbl 0625.35080Dobrokhotov, S. Yu.; Zhevandrov, P. N. 11 1985 Quantum and classical dynamics of an electron in thin curved tubes with spin and external electromagnetic fields taken into account. Zbl 1186.81061Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya. 10 2004 Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I: The Cauchy problem. Zbl 1146.35055Dobrokhotov, S. Yu.; Sinitsyn, S. O.; Tirozzi, B. 10 2007 Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems. Zbl 1441.81091Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 10 2019 “Momentum” tunneling between tori and the splitting of eigenvalues of the Laplace-Beltrami operator on Liouville surfaces. Zbl 0968.58025Dobrokhotov, S. Yu.; Shafarevich, A. I. 10 1999 Lagrangian manifolds related to the asymptotics of Hermite polynomials. Zbl 1409.42019Dobrokhotov, S. Yu.; Tsvetkova, A. V. 9 2018 Asymptotic solutions of linearized Navier-Stokes equations. Zbl 0816.76025Dobrokhotov, S. Yu.; Shafarevich, A. I. 9 1993 Unstable closed trajectories, librations and splitting of the lowest eigenvalues in quantum double well problem. Zbl 1164.81312Brüning, J.; Dobrokhotov, S. Yu.; Semenov, E. S. 9 2006 Maslov’s canonical operator, Hörmander’s formula, and localization of the Berry-Balazs solution in the theory of wave beams. Zbl 1323.81031Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E. 9 2014 Simple asymptotics for a generalized wave equation with degenerating velocity and their applications in the linear long wave run-up problem. Zbl 1420.35151Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 8 2018 A class of exact algebraic localized solutions of the multidimensional wave equation. Zbl 1234.35142Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya. 8 2010 Characteristics with singularities and the boundary values of the asymptotic solution of the Cauchy problem for a degenerate wave equation. Zbl 1362.35170Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 8 2016 Propagation of a linear wave created by a spatially localized perturbation in a regular lattice and punctured Lagrangian manifolds. Zbl 1376.37114Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 8 2017 Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential. Zbl 0799.35050Dobrokhotov, S. Yu.; Kolokol’tsov, V. N. 8 1993 Description of a tsunami wave propagation on the ground of the Maslov canonical operator. Zbl 1119.76311Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskij, T. Ya. 8 2006 On the behavior of an incompressible fluid velocity field at infinity. Zbl 0889.76011Dobrokhotov, S. Yu.; Shafarevich, A. I. 8 1996 Averaging of linear operators, adiabatic approximation, and pseudodifferential operators. Zbl 1282.47079Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu. 8 2012 The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory. Zbl 1200.53072Dobrokhotov, S. Yu.; Rouleux, M. 8 2010 Parametrix and asymptotics of localized solutions of Navier-Stokes equations in \(R^ 3\) linearized on a smooth flow. Zbl 0751.76020Dobrokhotov, S. Yu.; Shafarevich, A. I. 8 1992 Exact and asymptotic solutions of the Cauchy-Poisson problem with localized initial conditions and a constant function of the bottom. Zbl 1386.76082Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya.; Tolchennikov, A. A. 7 2017 Asymptotics of the solution of the Cauchy-Poisson problem in a layer of nonconstant thickness. Zbl 0810.35084Dobrokhotov, S. Yu.; Zhevandrov, P. N.; Kuz’mina, V. M. 7 1993 Asymptotic solutions of the Schrödinger equation in thin tubes. Zbl 1126.35354Belov, V. V.; Dobrokhotov, S. Yu.; Sinitsyn, S. O. 7 2003 Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source. Zbl 1293.35279Grushin, V. V.; Dobrokhotov, S. Yu.; Sergeev, S. A. 7 2013 The semi-classical Maupertuis-Jacobi correspondence for quasi-periodic Hamiltonian flows with applications to linear water waves theory. Zbl 1242.37042Dobrokhotov, Sergey; Rouleux, Michel 7 2011 Efficient formulas for the Maslov canonical operator near a simple caustic. Zbl 1406.81036Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 6 2018 On the asymptotics of a Bessel-type integral having applications in wave run-up theory. Zbl 1384.42001Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 6 2017 Uniform formulas for the asymptotic solution of a linear pseudodifferential equation describing water waves generated by a localized source. Zbl 1448.35391Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. 6 2020 The Maupertuis-Jacobi principle for Hamiltonians of the form \(F(x,|p|)\) in two-dimensional stationary semiclassical problems. Zbl 1360.37159Dobrokhotov, S. Yu.; Minenkov, D. S.; Rouleux, M. 6 2015 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 1059.76506Dobrokhotov, S. Yu. 6 1999 The double-well splitting of the low energy levels for the Schrödinger operator of discrete \(\varphi^ 4\)-models on tori. Zbl 0820.60097Dobrokhotov, Sergei Yu.; Kolokol’tsov, Vassili N. 6 1995 On transforms reducing one-dimensional systems of shallow-water to the wave equation with sound speed \(c^2=x\). Zbl 1307.76010Dobrokhotov, S. Yu.; Medvedev, S. B.; Minenkov, D. S. 6 2013 Asymptotic solutions of 2D wave equations with variable velocity and localized right-hand side. Zbl 1192.35110Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 6 2010 Resonances in asymptotic solutions of the Cauchy problem for the Schrödinger equation with rapidly oscillating finite-zone potential. Zbl 0667.35058Dobrokhotov, S. Yu. 6 1988 Lagrangian manifolds and efficient short-wave asymptotics in a neighborhood of a caustic cusp. Zbl 1483.53094Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 5 2020 Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber. Zbl 1411.81090Dobrokhotov, S. Yu.; Minenkov, D. S.; Shlosman, S. B. 5 2018 On various averaging methods for a nonlinear oscillator with slow time-dependent potential and a nonconservative perturbation. Zbl 1209.34050Dobrokhotov, S. Yu.; Minenkov, D. S. 5 2010 Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data. Zbl 1230.35057Dobrokhotov, S. Yu.; Nazaĭkinskiĭ, V. E.; Tirozzi, B. 5 2011 Asymptotics of linear water waves generated by a localized source near the focal points on the leading edge. Zbl 1432.76203Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. 5 2017 The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides. Zbl 1377.35062Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Rouleux, M. 5 2017 Maslov’s canonical operator in arbitrary coordinates on the Lagrangian manifold. Zbl 1345.53083Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Shafarevich, A. I. 5 2016 Isotropic tori, complex germ and Maslov index, normal forms and quasimodes of multidimensional spectral problems. Zbl 1013.58014Belov, V. V.; Dobrokhotov, O. S.; Dobrokhotov, S. Yu. 5 2001 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 1194.35054Bianchi, D.; Dobrokhotov, S. Yu.; Tirozzi, B. 5 2008 The spectral asymptotics of the two-dimensional Schrödinger operator with a strong magnetic field. II. Zbl 1104.81307Brüning, J.; Dobrokhotov, S. Yu.; Pankrashkin, K. V. 5 2002 Electronic optics in graphene in the semiclassical approximation. Zbl 1397.78009Reijnders, K. J. A.; Minenkov, D. S.; Katsnelson, M. I.; Dobrokhotov, S. Yu. 5 2018 Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. Zbl 1263.35154Dobrokhotov, Sergey; Minenkov, Dmitrii; Nazaikinskii, Vladimir; Tirozzi, Brunello 5 2013 Peierls substitution and the Maslov operator method. Zbl 1197.35086Grushin, V. V.; Dobrokhotov, S. Yu. 5 2010 “Operator separation of variables” in problems of short-wave asymptotic behavior for differential equations with fast oscillating coefficients. Zbl 0671.35013Berlyand, L. V.; Dobrokhotov, S. Yu. 5 1987 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 1426.37049Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 4 2019 Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity. Zbl 1145.81351Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V.; Shafarevich, A. I. 4 2008 Generalized Foldy-Wouthuysen transformation and pseudodifferential operators. Zbl 1274.81069Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya. 4 2011 Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections. Zbl 1359.76057Dobrokhotov, S. Yu.; Grushin, V. V.; Sergeev, S. A.; Tirozzi, B. 4 2016 Volume and entropy in abstract analytic number theory and thermodynamics. Zbl 1362.82025Maslov, V. P.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 4 2016 Explicit formulas for generalized action-angle variables in a neighborhood of an isotropic torus and their application. Zbl 1178.37055Belov, V. V.; Dobrokhotov, S. Yu.; Maksimov, V. A. 4 2003 Splitting of lower energy levels in a quantum double well in a magnetic field and tunneling of wave packets in nanowires. Zbl 1286.81057Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V. 4 2013 Asymptotics of shallow water equations on the sphere. Zbl 1311.76012Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A. 4 2014 Approximate formulas for eigenvalues of the Laplace operator on a torus arising in linear problems with oscillating coefficients. Zbl 1257.35135Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu. 4 2012 Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms. Zbl 1297.76027Chirkunov, Yu. A.; Dobrokhotov, S. Yu.; Medvedev, S. B.; Minenkov, D. S. 4 2014 Magnetic field asymptotics in a well conducting fluid. Zbl 1181.76152Dobrokhotov, Sergei; Olive, Victor M.; Ruzmaikin, Alexander; Shafarevich, Andrei 4 1996 Asymptotics of waves on the shallow water generated by spatially-localized sources and trapped by underwater ridges. Zbl 1276.76011Dobrokhotov, S. Yu.; Lozhnikov, D. A.; Vargas, C. A. 3 2013 Uniform asymptotics of the boundary values of the solution in a linear problem on the run-up of waves on a shallow beach. Zbl 1372.35180Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. 3 2017 Quantization of the Bellman equation, exponential asymptotics and tunneling. Zbl 0796.35141Dobrokhotov, S. Yu.; Kolokoltsov, V. N.; Maslov, V. P. 3 1992 Cauchy–Riemann conditions and localized asymptotic solutions of linearized equations of shallow water theory. Zbl 1100.76506Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 3 2005 Quantum dynamics in a thin film. I: Propagation of localized perturbations. Zbl 1175.81117Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tudorovskiy, T. Ya. 3 2008 Splitting formulas for the higher and lower energy levels of the one-dimensional Schrödinger operator. Zbl 1178.81070Albeverio, S.; Dobrokhotov, S. Yu.; Semenov, E. S. 3 2004 Solution of the two-dimensional Dirac equation with a linear potential and a localized initial condition. Zbl 1417.81126Dobrokhotov, S. Yu.; Tolchennikov, A. A. 3 2019 Uniformization of equations with Bessel-type boundary degeneration and semiclassical asymptotics. Zbl 1455.76019Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 3 2020 On a homogenization method for differential operators with oscillating coefficients. Zbl 1326.35022Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 3 2015 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 1060.76533Dobrokhotov, S. Yu. 3 1999 The short-wave asymptotics in a linearized system of equations of hydrodynamics with rapidly varying coefficients. Zbl 0850.35076Dobrokhotov, S. Yu; Shafarevich, A. I. 3 1988 The Maslov canonical operator on isotropic manifolds with a complex germ, and its applications to spectral problems. Zbl 0686.58015Belov, V. V.; Dobrokhotov, S. Yu. 3 1988 Semiclassical asymptotic behavior of the scattering of wave packets by the rapidly changing potential given by the equation \(-2| \nabla \Phi | ^ 2/\cosh ^ 2[\Phi (X)/h]+V_ 0(X)\). Zbl 0696.35125Dobrokhotov, S. Yu.; Shafarevich, A. I. 3 1987 Diophantine tori and pragmatic calculation of quasimodes for operators with integrable principal symbol. Zbl 1452.37071Anikin, A. Yu.; Dobrokhotov, S. Yu. 2 2020 Asymptotic solution of the Helmholtz equation in a three-dimensional layer of variable thickness with a localized right-hand side. Zbl 1433.35019Petrov, P. N.; Dobrokhotov, S. Yu. 2 2019 Remark on the phase shift in the Kuzmak-Whitham ansatz. Zbl 1274.35356Dobrokhotov, S. Yu.; Minenkov, D. S. 2 2011 Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations. Zbl 1492.81056Dobrokhotov, Sergey Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I. 2 2021 Canonical operator on punctured Lagrangian manifolds. Zbl 1462.35480Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Schafarevich, A. I. 2 2021 An approach to finding the asymptotics of polynomials given by recurrence relations. Zbl 1467.42041Dobrokhotov, S. Yu.; Tsvetkova, A. V. 1 2021 Representation of Bessel functions by the Maslov canonical operator. Zbl 1471.81033Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E. 1 2021 Uniform formulas for the asymptotic solution of a linear pseudodifferential equation describing water waves generated by a localized source. Zbl 1448.35391Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. 6 2020 Lagrangian manifolds and efficient short-wave asymptotics in a neighborhood of a caustic cusp. Zbl 1483.53094Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 5 2020 Uniformization of equations with Bessel-type boundary degeneration and semiclassical asymptotics. Zbl 1455.76019Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 3 2020 Diophantine tori and pragmatic calculation of quasimodes for operators with integrable principal symbol. Zbl 1452.37071Anikin, A. Yu.; Dobrokhotov, S. Yu. 2 2020 Airy functions and transition between semiclassical and harmonic oscillator approximations for one-dimensional bound states. Zbl 1453.81024Anikin, A. Yu.; Dobrokhotov, S. Yu.; Tsvetkova, A. V. 2 2020 Efficient asymptotics in problems on the propagation of waves generated by localized sources in linear multidimensional inhomogeneous and dispersive media. Zbl 1450.35119Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 1 2020 Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems. Zbl 1441.81091Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 10 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 1426.37049Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 4 2019 Solution of the two-dimensional Dirac equation with a linear potential and a localized initial condition. Zbl 1417.81126Dobrokhotov, S. Yu.; Tolchennikov, A. A. 3 2019 Asymptotic solution of the Helmholtz equation in a three-dimensional layer of variable thickness with a localized right-hand side. Zbl 1433.35019Petrov, P. N.; Dobrokhotov, S. Yu. 2 2019 Nonstandard Lagrangian singularities and asymptotic eigenfunctions of the degenerating operator \(- \frac{d}{dx}D (x)\frac{d}{dx}\). Zbl 1452.34085Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 2 2019 Classical and quantum dynamics of a particle in a narrow angle. Zbl 1434.35135Dobrokhotov, Sergei Yu.; Minenkov, Dmitrii S.; Neishtadt, Anatoly I.; Shlosman, Semen B. 1 2019 Averaging and spectral bands for the 2-D magnetic Schrödinger operator with growing and one-direction periodic potential. Zbl 1426.81034Anikin, A. Yu.; Brüning, J.; Dobrokhotov, S. Yu.; Vybornyi, E. V. 1 2019 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. Zbl 1418.37094Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 1 2019 Lagrangian manifolds related to the asymptotics of Hermite polynomials. Zbl 1409.42019Dobrokhotov, S. Yu.; Tsvetkova, A. V. 9 2018 Simple asymptotics for a generalized wave equation with degenerating velocity and their applications in the linear long wave run-up problem. Zbl 1420.35151Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 8 2018 Efficient formulas for the Maslov canonical operator near a simple caustic. Zbl 1406.81036Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 6 2018 Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber. Zbl 1411.81090Dobrokhotov, S. Yu.; Minenkov, D. S.; Shlosman, S. B. 5 2018 Electronic optics in graphene in the semiclassical approximation. Zbl 1397.78009Reijnders, K. J. A.; Minenkov, D. S.; Katsnelson, M. I.; Dobrokhotov, S. Yu. 5 2018 Waves on the free surface described by linearized equations of hydrodynamics with localized right-hand sides. Zbl 1388.76028Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 2 2018 Influence of the elastic base of a basin on the propagation of waves on the water surface. Zbl 1432.76059Dobrokhotov, S. Yu.; Tolstova, O. L.; Sekerzh-Zenkovich, S. Ya.; Vargas, C. A. 1 2018 Exact step-like solutions of one-dimensional shallow-water equations over a sloping bottom. Zbl 1415.35226Aksenov, A. V.; Dobrokhotov, S. Yu.; Druzhkov, K. P. 1 2018 Punctured Lagrangian manifolds and asymptotic solutions of the linear water wave equations with localized initial conditions. Zbl 06769034Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 20 2017 New integral representations of the Maslov canonical operator in singular charts. Zbl 1369.81033Dobrokhotov, Sergei Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I. 19 2017 Propagation of a linear wave created by a spatially localized perturbation in a regular lattice and punctured Lagrangian manifolds. Zbl 1376.37114Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 8 2017 Exact and asymptotic solutions of the Cauchy-Poisson problem with localized initial conditions and a constant function of the bottom. Zbl 1386.76082Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya.; Tolchennikov, A. A. 7 2017 On the asymptotics of a Bessel-type integral having applications in wave run-up theory. Zbl 1384.42001Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 6 2017 Asymptotics of linear water waves generated by a localized source near the focal points on the leading edge. Zbl 1432.76203Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. 5 2017 The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides. Zbl 1377.35062Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Rouleux, M. 5 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 1372.35180Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. 3 2017 Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics. Zbl 1393.82023Anikin, A. Yu.; Dobrokhotov, S. Yu.; Klevin, A. I.; Tirozzi, B. 2 2017 Averaging and trajectories of a Hamiltonian system appearing in graphene placed in a strong magnetic field and a periodic potential. Zbl 1394.82019Anikin, A.; Brüning, J.; Dobrokhotov, S. Yu. 1 2017 Characteristics with singularities and the boundary values of the asymptotic solution of the Cauchy problem for a degenerate wave equation. Zbl 1362.35170Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 8 2016 Maslov’s canonical operator in arbitrary coordinates on the Lagrangian manifold. Zbl 1345.53083Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Shafarevich, A. I. 5 2016 Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections. Zbl 1359.76057Dobrokhotov, S. Yu.; Grushin, V. V.; Sergeev, S. A.; Tirozzi, B. 4 2016 Volume and entropy in abstract analytic number theory and thermodynamics. Zbl 1362.82025Maslov, V. P.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 4 2016 Maslov complex germ and high-frequency Gaussian beams for cold plasma in a toroidal domain. Zbl 1354.82032Dobrokhotov, S. Yu.; Cardinali, A.; Klevin, A. I.; Tirozzi, Brunello 2 2016 Simple exact and asymptotic solutions of the 1D run-up problem over a slowly varying (quasiplanar) bottom. Zbl 1329.35246Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E.; Tirozzi, B. 2 2016 Lower part of the spectrum for the two-dimensional Schrödinger operator periodic in one variable and application to quantum dimers. Zbl 1349.81096Anikin, A. Yu.; Dobrokhotov, S. Yu.; Katsnelson, M. I. 1 2016 Approximation of solutions of the two-dimensional wave equation with variable velocity and localized right-hand side using some “simple” solutions. Zbl 1362.35169Dobrokhotov, S. Yu.; Anikin, A. Yu. 1 2016 Semiclassical asymptotic approximations and the density of states for the two-dimensional radially symmetric Schrödinger and Dirac equations in tunnel microscopy problems. Zbl 1338.81182Brüning, J.; Dobrokhotov, S. Yu.; Katsnelson, M. I.; Minenkov, D. S. 1 2016 New representations of the Maslov canonical operator and localized asymptotic solutions for strictly hyperbolic systems. Zbl 1331.35219Allilueva, A. I.; Dobrokhotov, S. Yu.; Sergeev, S. A.; Shafarevich, A. I. 13 2015 The Maupertuis-Jacobi principle for Hamiltonians of the form \(F(x,|p|)\) in two-dimensional stationary semiclassical problems. Zbl 1360.37159Dobrokhotov, S. Yu.; Minenkov, D. S.; Rouleux, M. 6 2015 On a homogenization method for differential operators with oscillating coefficients. Zbl 1326.35022Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 3 2015 Maslov’s canonical operator, Hörmander’s formula, and localization of the Berry-Balazs solution in the theory of wave beams. Zbl 1323.81031Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E. 9 2014 Asymptotics of shallow water equations on the sphere. Zbl 1311.76012Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A. 4 2014 Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms. Zbl 1297.76027Chirkunov, Yu. A.; Dobrokhotov, S. Yu.; Medvedev, S. B.; Minenkov, D. S. 4 2014 Homogenization in the problem of long water waves over a bottom site with fast oscillations. Zbl 1315.35165Grushin, V. V.; Dobrokhotov, S. Yu. 2 2014 Fourier integrals and a new representation of Maslov’s canonical operator near caustics. Zbl 1320.81058Dobrokhotov, S. Yu.; Makrakis, G.; Nazaikinskii, V. E. 2 2014 New formulas for Maslov’s canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics. Zbl 1298.81091Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E.; Tudorovskii, T. Ya. 22 2013 Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data. Zbl 1320.35180Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 13 2013 Asymptotic solutions of the Cauchy problem with localized initial conditions for linearized two-dimensional Boussinesq-type equations with variable coefficients. Zbl 1276.76012Dobrokhotov, S. Yu.; Sergeev, S. A.; Tirozzi, B. 12 2013 Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source. Zbl 1293.35279Grushin, V. V.; Dobrokhotov, S. Yu.; Sergeev, S. A. 7 2013 On transforms reducing one-dimensional systems of shallow-water to the wave equation with sound speed \(c^2=x\). Zbl 1307.76010Dobrokhotov, S. Yu.; Medvedev, S. B.; Minenkov, D. S. 6 2013 Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. Zbl 1263.35154Dobrokhotov, Sergey; Minenkov, Dmitrii; Nazaikinskii, Vladimir; Tirozzi, Brunello 5 2013 Splitting of lower energy levels in a quantum double well in a magnetic field and tunneling of wave packets in nanowires. Zbl 1286.81057Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V. 4 2013 Asymptotics of waves on the shallow water generated by spatially-localized sources and trapped by underwater ridges. Zbl 1276.76011Dobrokhotov, S. Yu.; Lozhnikov, D. A.; Vargas, C. A. 3 2013 Averaging of linear operators, adiabatic approximation, and pseudodifferential operators. Zbl 1282.47079Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu. 8 2012 Approximate formulas for eigenvalues of the Laplace operator on a torus arising in linear problems with oscillating coefficients. Zbl 1257.35135Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu. 4 2012 Asymptotic solutions of the linear shallow-water equations with localized initial data. Zbl 1325.76036Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tirozzi, B. 17 2011 The semi-classical Maupertuis-Jacobi correspondence for quasi-periodic Hamiltonian flows with applications to linear water waves theory. Zbl 1242.37042Dobrokhotov, Sergey; Rouleux, Michel 7 2011 Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data. Zbl 1230.35057Dobrokhotov, S. Yu.; Nazaĭkinskiĭ, V. E.; Tirozzi, B. 5 2011 Generalized Foldy-Wouthuysen transformation and pseudodifferential operators. Zbl 1274.81069Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya. 4 2011 Remark on the phase shift in the Kuzmak-Whitham ansatz. Zbl 1274.35356Dobrokhotov, S. Yu.; Minenkov, D. S. 2 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 1251.35099Brüning, J.; Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya.; Tudorovskiy, T. Ya. 1 2011 Some solutions of the 3D Laplace equation in a layer with oscillating boundary describing an array of nanotubes and an application to cold field emission. I: Regular array. Zbl 1326.35114Brüning, J.; Dobrokhotov, S. Yu.; Minenkov, D. S. 1 2011 Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I. Zbl 1387.35404Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 26 2010 Localized solutions of one-dimensional non-linear shallow-water equations with velocity \(c=\sqrt x\). Zbl 1196.35161Dobrokhotov, S. Yu; Tirozzi, B. 14 2010 A class of exact algebraic localized solutions of the multidimensional wave equation. Zbl 1234.35142Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya. 8 2010 The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory. Zbl 1200.53072Dobrokhotov, S. Yu.; Rouleux, M. 8 2010 Asymptotic solutions of 2D wave equations with variable velocity and localized right-hand side. Zbl 1192.35110Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 6 2010 On various averaging methods for a nonlinear oscillator with slow time-dependent potential and a nonconservative perturbation. Zbl 1209.34050Dobrokhotov, S. Yu.; Minenkov, D. S. 5 2010 Peierls substitution and the Maslov operator method. Zbl 1197.35086Grushin, V. V.; Dobrokhotov, S. Yu. 5 2010 Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations. Zbl 1178.35301Dobrokhotov, S. Yu.; Tirozzi, B.; Vargas, C. A. 17 2009 Quantum dynamics in a thin film. II: Stationary states. Zbl 1182.81038Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V. 1 2009 Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations. Zbl 1180.35336Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B. 46 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 1194.35054Bianchi, D.; Dobrokhotov, S. Yu.; Tirozzi, B. 5 2008 Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity. Zbl 1145.81351Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V.; Shafarevich, A. I. 4 2008 Quantum dynamics in a thin film. I: Propagation of localized perturbations. Zbl 1175.81117Brüning, J.; Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tudorovskiy, T. Ya. 3 2008 Representations of rapidly decaying functions by the Maslov canonical operator. Zbl 1344.58014Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 28 2007 Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I: The Cauchy problem. Zbl 1146.35055Dobrokhotov, S. Yu.; Sinitsyn, S. O.; Tirozzi, B. 10 2007 Operator separation of variables for adiabatic problems in quantum and wave mechanics. Zbl 1110.81080Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskiy, T. Ya. 32 2006 Description of tsunami propagation based on the Maslov canonical operator. Zbl 1152.35089Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskii, T. Ya. 13 2006 Unstable closed trajectories, librations and splitting of the lowest eigenvalues in quantum double well problem. Zbl 1164.81312Brüning, J.; Dobrokhotov, S. Yu.; Semenov, E. S. 9 2006 Description of a tsunami wave propagation on the ground of the Maslov canonical operator. Zbl 1119.76311Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskij, T. Ya. 8 2006 Spectral series of the Schrödinger operator in thin waveguides with periodic structure. I: Adiabatic approximation and semiclassical asymptotics in the 2D case. Zbl 1113.81031Brüning, J.; Dobrokhotov, S.; Sekerzh-Zenkovich, S.; Tudorovskiy, T. 1 2006 Cauchy–Riemann conditions and localized asymptotic solutions of linearized equations of shallow water theory. Zbl 1100.76506Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 3 2005 A perturbative theory of the evolution of the center of typhoons. Zbl 1169.86307Dobrokhotov, Sergey; Semenov, Evgeny; Tirozzi, Brunello 2 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 1190.81136Brüning, J.; Dobrokhotov, S. Yu.; Geyler, V. A.; Tudorovskiy, T. Ya. 1 2005 On quasimodes of small diffusion operators corresponding to stable invariant tori with nonregular neighborhoods. Zbl 1192.35040Albeverio, Sergio; Dobrokhotov, Sergey; Poteryakhin, Michael 1 2005 Asymptotic solutions of nonrelativistic equations of quantum mechanics in curved nanotubes. I: Reduction to spatially one-dimensional equations. Zbl 1178.81080Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya. 15 2004 Quantum and classical dynamics of an electron in thin curved tubes with spin and external electromagnetic fields taken into account. Zbl 1186.81061Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya. 10 2004 Splitting formulas for the higher and lower energy levels of the one-dimensional Schrödinger operator. Zbl 1178.81070Albeverio, S.; Dobrokhotov, S. Yu.; Semenov, E. S. 3 2004 On normal forms in a neighborhood of two-dimensional resonance tori for a multidimensional anharmonic oscillator. Zbl 1083.34031Dobrokhotov, S. Yu.; Poteryakhin, M. A. 2 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 1065.76026Dobrokhotov, S. Yu.; Zhevandrov, P. N. 19 2003 Asymptotic solutions of the Schrödinger equation in thin tubes. Zbl 1126.35354Belov, V. V.; Dobrokhotov, S. Yu.; Sinitsyn, S. O. 7 2003 ...and 59 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 267 Authors 98 Dobrokhotov, Sergei Yurievich 40 Nazaikinskii, Vladimir E. 37 Shafarevich, Andreĭ Igorevich 19 Anikin, A. Yu. 19 Tirozzi, Brunello 16 Maslov, Viktor Pavlovich 15 Allilueva, Anna I. 15 Sergeev, Sergeĭ Alekseevich 14 Grushin, V. V. 14 Tolchennikov, Anton A. 12 Brüning, Jochen 12 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 12 Tsvetkova, Anna V. 11 Minenkov, Dmitrii S. 8 Vybornyi, E. V. 7 Klevin, A. I. 6 Kalyakin, Leonid Anatol’evich 6 Rabinovich, Vladimir Samuilovich 5 Bulatov, Vitaliĭ Vasil’evich 5 Helffer, Bernard 5 Karasev, Mikhail Vladimirovich 5 Kucherenko, Valeri V. 5 Miller, Peter D. 5 Tudorovskii, T. Ya. 5 Zhevandrov, Peter N. 4 Belov, Vladimir Vasilyevich 4 Lozhnikov, D. A. 4 Mal’tsev, Andreĭ Yakovlevich 4 Nekrasov, R. V. 4 Petrov, Pavel S. 4 Sultanov, Oskar A. 4 Vorob’ev, Yu. M. 3 Aida, Shigeki 3 Brandolese, Lorenzo 3 Fedotov, Alexander 3 Kordyukov, Yuri A. 3 Kryvko, Andriy 3 Kuksin, Sergeĭ B. 3 Pereskokov, A. V. 3 Tolstova, O. L. 3 Topalov, Peter J. 3 Vargas, Carlos A. 3 Vladimirov, I. Yu. 3 Volkov, B. I. 3 Wilkening, Jon A. 2 Babich, Vasiliĭ Mikhaĭlovich 2 Bikbaev, Ramil’ F. 2 Borisov, Denis Ivanovich 2 Brezhnev, Yurii V. 2 Chang, Tongkeun 2 Chirkunov, Yuriĭ Aleksandrovich 2 Dell’Antonio, Gian Fausto 2 Dubrovin, Boris Anatol’evich 2 El, Gennady A. 2 Haberman, Richard 2 Hu, Chinkun 2 Jin, Bumja 2 Kabanikhin, Sergeĭ Igorevich 2 Katsnelson, Mikhail I. 2 Klopp, Frédéric 2 Konishi, Eiji 2 Krichever, Igor’ Moiseevich 2 Krivorotko, Olga I. 2 Kukavica, Igor 2 Kulikovskiĭ, Andreĭ Gennad’evich 2 Makrakis, George N. 2 Maksimov, V. A. 2 McOwen, Robert C. 2 Medvedev, Sergeĭ Borisovich 2 Moll, Alexander C. 2 Neĭshtadt, Anatoliĭ Iserovich 2 Novikova, E. M. 2 Pankrashkin, Konstantin 2 Pelinovsky, Efim 2 Perel, Maria V. 2 Petrov, P. N. 2 Qin, Yuming 2 Rodríguez Bermúdez, Panters 2 Rodríguez, M. I. Romero 2 Rouleux, Michel 2 Rozanova, Olga S. 2 Smyth, Noel Frederick 2 Valiño Alonso, Baldomero 2 Wetzel, Alfredo N. 2 Yu, Jui-Ling 2 Zhang, Jianlin 2 Zhao, Xinyu 1 Abenda, Simonetta 1 Abramian, Andrei K. 1 Agafonov, Sergey I. 1 Albeverio, Sergio A. 1 Alvarez, Gustavo Benitez 1 Ambrose, David M. 1 Arora, Sumit 1 Avendaño-Camacho, Misael 1 Azado, P. C. 1 Azhotkin, V. D. 1 Barrera-Figueroa, Victor 1 Bestuzheva, Alla Nikolaevna 1 Bianchi, Daniela ...and 167 more Authors all top 5 Cited in 74 Serials 82 Russian Journal of Mathematical Physics 70 Mathematical Notes 35 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 Soviet Mathematics 6 Fluid Dynamics 6 Journal of Applied Mathematics and Mechanics 6 Journal of Mathematical Sciences (New York) 5 Functional Analysis and its Applications 5 Journal of Functional Analysis 4 Applicable Analysis 4 Journal of Fluid Mechanics 4 Prikladnaya Matematika i Mekhanika 4 Computational Mathematics and Mathematical Physics 4 Regular and Chaotic Dynamics 4 Differential Equations 3 Communications in Mathematical Physics 3 Journal of Differential Equations 3 St. Petersburg Mathematical Journal 2 International Journal of Modern Physics A 2 Journal of Engineering Mathematics 2 Mathematical Methods in the Applied Sciences 2 Russian Mathematical Surveys 2 ZAMP. 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