Edit Profile (opens in new tab) Dobrokhotov, Sergei Yurievich Co-Author Distance Author ID: dobrokhotov.sergei-yu Published as: Dobrokhotov, S. Yu.; Dobrokhotov, Sergei Yu.; Dobrokhotov, Sergey; Dobrokhotov, Sergey Yu.; Dobrokhotov, S.; 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: 241 Publications since 1975, including 7 Additional arXiv Preprints 1 Contribution as Editor Co-Authors: 155 Co-Authors with 227 Joint Publications 4,037 Co-Co-Authors all top 5 Co-Authors 13 single-authored 45 Nazaikinskii, Vladimir E. 33 Tirozzi, Brunello 26 Shafarevich, Andreĭ Igorevich 24 Brüning, Jochen 24 Maslov, Viktor Pavlovich 17 Anikin, A. Yu. 14 Minenkov, Dmitrii S. 12 Tsvetkova, Anna V. 10 Belov, Vladimir Vasilyevich 10 Rouleux, Michel 10 Tolchennikov, Anton A. 10 Tudorovskii, T. Ya. 9 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 8 Grushin, V. V. 8 Pankrashkin, Konstantin 8 Semenov, E. S. 7 Sergeev, Sergeĭ Alekseevich 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. 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 Anikin, Anatoly Y. 2 Chebotarev, Alexandr M. 2 Chernous’ko, Feliks Leonidovich 2 Geyler, Vladimir A. 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 Nosikov, I. A. 2 Pavlov, Boris Sergeevich 2 Petrov, P. N. 2 Shkalikov, Andreĭ Andreevich 2 Sinitsyn, S. O. 2 Sturova, Izolda V. 1 Aksenov, Alexander V. 1 Allilueva, Anna I. 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, Konstantin P. 1 Escamilla Reyna, Juan Alberto 1 Exner, Pavel 1 Fradkin, L. Yu. 1 Frost, V. A. 1 Gershtein, S. S. 1 Grinevich, Pëtr Georgievich 1 Griniv, R. O. 1 Grushevsky, Samuel 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 Levin, Sergei B. 1 Libanov, M. V. 1 Lukin, Dmitry S. 1 Martines Olive, Victor 1 Martinez-Olive, W. ...and 55 more Co-Authors all top 5 Serials 53 Russian Journal of Mathematical Physics 42 Mathematical Notes 30 Theoretical and Mathematical Physics 12 Doklady Mathematics 9 Russian Mathematical Surveys 6 Doklady Akademii Nauk 5 Journal of Soviet Mathematics 5 Soviet Physics. Doklady 4 Functional Analysis and its Applications 4 Proceedings of the Steklov Institute of Mathematics 3 Matematicheskie Zametki 3 Computational Mathematics and Mathematical Physics 3 Journal of Mathematical Sciences (New York) 3 St. Petersburg Mathematical Journal 3 Regular and Chaotic Dynamics 2 Fluid Dynamics 2 Journal of Engineering Mathematics 2 Funktsional’nyĭ Analiz i ego Prilozheniya 2 Asymptotic Analysis 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 149 Partial differential equations (35-XX) 71 Fluid mechanics (76-XX) 64 Quantum theory (81-XX) 31 Dynamical systems and ergodic theory (37-XX) 22 Ordinary differential equations (34-XX) 21 Geophysics (86-XX) 20 Differential geometry (53-XX) 12 Mechanics of particles and systems (70-XX) 12 Statistical mechanics, structure of matter (82-XX) 11 Special functions (33-XX) 10 Operator theory (47-XX) 8 History and biography (01-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 Algebraic geometry (14-XX) 3 Difference and functional equations (39-XX) 2 General and overarching topics; collections (00-XX) 2 Approximations and expansions (41-XX) 2 Manifolds and cell complexes (57-XX) 2 Probability theory and stochastic processes (60-XX) 1 Number theory (11-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 172 Publications have been cited 1,160 times in 407 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. 48 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. 37 2006 Representations of rapidly decaying functions by the Maslov canonical operator. Zbl 1344.58014 Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 30 2007 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. 26 2010 New integral representations of the Maslov canonical operator in singular charts. Zbl 1369.81033 Dobrokhotov, Sergei Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I. 26 2017 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. 25 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. 22 2013 Punctured Lagrangian manifolds and asymptotic solutions of the linear water wave equations with localized initial conditions. Zbl 1516.35040 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 21 2017 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. 21 2019 Maslov’s methods in the linearized theory of gravitational waves on a fluid surface. Zbl 0533.76013 Dobrokhotov, S. Yu. 20 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 1065.76026 Dobrokhotov, S. Yu.; Zhevandrov, P. N. 20 2003 Multi-phase solutions of the Benjamin-Ono equation and their averaging. Zbl 0752.35058 Dobrokhotov, S. Yu.; Krichever, I. M. 20 1991 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. 18 1994 Finite-zone, almost-periodic solutions in WKB approximations. Zbl 0461.35010 Dobrokhotov, S. Yu.; Maslov, V. P. 18 1981 Asymptotic solutions of the linear shallow-water equations with localized initial data. Zbl 1325.76036 Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tirozzi, B. 17 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. 17 2009 Finite-zone almost periodic solutions in WKB-approximations. (Endlichzonige fastperiodische Lösungen in WKB-Approximationen.) Zbl 0446.35008 Dobrokhotov, S. Yu.; Maslov, V. P. 16 1980 Localized solutions of one-dimensional non-linear shallow-water equations with velocity \(c=\sqrt x\). Zbl 1196.35161 Dobrokhotov, S. Yu; Tirozzi, B. 16 2010 Multiphase asymptotics of nonlinear partial differential equations with a small parameter. Zbl 0551.35072 Dobrokhotov, 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 1178.81080 Belov, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya. 15 2004 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. 15 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. 15 2015 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. 15 2018 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. 13 2006 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. 13 2002 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. 13 2013 Nonstandard characteristics and Maslov’s operational method in linear problems concerning unsteady water waves. Zbl 0625.35080 Dobrokhotov, S. Yu.; Zhevandrov, P. N. 12 1985 Lagrangian manifolds related to the asymptotics of Hermite polynomials. Zbl 1409.42019 Dobrokhotov, S. Yu.; Tsvetkova, A. V. 12 2018 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. 12 2013 Averaging of linear operators, adiabatic approximation, and pseudodifferential operators. Zbl 1282.47079 Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu. 12 2012 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. 11 2007 A class of exact algebraic localized solutions of the multidimensional wave equation. Zbl 1234.35142 Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya. 11 2010 “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. 11 1999 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. 11 2006 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. 11 1993 Averaging for Hamiltonian systems with one fast phase and small amplitudes. Zbl 1025.37038 Brüning, Jochen; Dobrokhotov, S. Yu.; Poteryakhin, M. A. 11 2001 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. 10 2004 Asymptotic solutions of linearized Navier-Stokes equations. Zbl 0816.76025 Dobrokhotov, S. Yu.; Shafarevich, A. I. 10 1993 Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations. Zbl 1492.81056 Dobrokhotov, Sergey Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I. 10 2021 Resonances in asymptotic solutions of the Cauchy problem for the Schrödinger equation with rapidly oscillating finite-zone potential. Zbl 0667.35058 Dobrokhotov, S. Yu. 9 1988 On the asymptotics of a Bessel-type integral having applications in wave run-up theory. Zbl 1384.42001 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 9 2017 On the behavior of an incompressible fluid velocity field at infinity. Zbl 0889.76011 Dobrokhotov, S. Yu.; Shafarevich, A. I. 9 1996 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. 9 2014 The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory. Zbl 1200.53072 Dobrokhotov, S. Yu.; Rouleux, M. 9 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. 8 2006 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. 8 2017 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. 8 1995 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 8 2011 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. 8 1992 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. 8 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. 8 2016 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. 8 1999 Lagrangian manifolds and efficient short-wave asymptotics in a neighborhood of a caustic cusp. Zbl 1483.53094 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 8 2020 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. 8 2018 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. 8 2020 Efficient formulas for the Maslov canonical operator near a simple caustic. Zbl 1406.81036 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 8 2018 Asymptotic solutions of the Schrödinger equation in thin tubes. Zbl 1126.35354 Belov, V. V.; Dobrokhotov, S. Yu.; Sinitsyn, S. O. 7 2003 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. 7 1993 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. 7 2014 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. 7 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. 7 2016 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. 7 2015 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. 7 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. 7 2013 Electronic optics in graphene in the semiclassical approximation. Zbl 1397.78009 Reijnders, K. J. A.; Minenkov, D. S.; Katsnelson, M. I.; Dobrokhotov, S. Yu. 7 2018 “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. 6 1987 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. 6 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. 6 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. 6 2002 On a homogenization method for differential operators with oscillating coefficients. Zbl 1326.35022 Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 6 2015 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. 5 2010 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. 5 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. 5 2017 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. 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 1194.35054 Bianchi, D.; Dobrokhotov, S. Yu.; Tirozzi, B. 5 2008 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. 5 2019 Uniformization of equations with Bessel-type boundary degeneration and semiclassical asymptotics. Zbl 1455.76019 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 5 2020 Peierls substitution and the Maslov operator method. Zbl 1197.35086 Grushin, V. V.; Dobrokhotov, S. Yu. 5 2010 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. 5 2012 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 5 2013 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. 4 2003 Magnetic field asymptotics in a well conducting fluid. Zbl 1181.76152 Dobrokhotov, Sergei; Olive, Victor M.; Ruzmaikin, Alexander; Shafarevich, Andrei 4 1996 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. 4 1994 Quantization of the Bellman equation, exponential asymptotics and tunneling. Zbl 0796.35141 Dobrokhotov, S. Yu.; Kolokoltsov, V. N.; Maslov, V. P. 4 1992 Asymptotics of shallow water equations on the sphere. Zbl 1311.76012 Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A. 4 2014 Volume and entropy in abstract analytic number theory and thermodynamics. Zbl 1362.82025 Maslov, V. P.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 4 2016 Maslov’s canonical operator in arbitrary coordinates on the Lagrangian manifold. Zbl 1345.53083 Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Shafarevich, A. I. 4 2016 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. 4 2008 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. 4 1999 Airy functions and transition between semiclassical and harmonic oscillator approximations for one-dimensional bound states. Zbl 1453.81024 Anikin, A. Yu.; Dobrokhotov, S. Yu.; Tsvetkova, A. V. 4 2020 Generalized Foldy-Wouthuysen transformation and pseudodifferential operators. Zbl 1274.81069 Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya. 4 2011 Nonstandard Lagrangian singularities and asymptotic eigenfunctions of the degenerating operator \(- \frac{d}{dx}D (x)\frac{d}{dx}\). Zbl 1452.34085 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 4 2019 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. 4 2013 Nonlocal analogs of the nonlinear Boussinesq equation for surface waves over a rough bottom, and their asymptotic solutions. Zbl 0626.76023 Dobrokhotov, S. Yu. 3 1987 The Maslov canonical operator on isotropic manifolds with a complex germ, and its applications to spectral problems. Zbl 0686.58015 Belov, V. V.; Dobrokhotov, S. Yu. 3 1988 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. 3 2004 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. 3 2017 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. 3 2008 On the Hamiltonian property of truncated Hugoniot-Maslov chains for trajectories of mesoscale vortices. Zbl 1074.76530 Dobrokhotov, S. Yu.; Tirozzi, B. 3 2002 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. 3 2005 Lagrangian manifolds and the construction of asymptotics for (pseudo)differential equations with localized right-hand sides. Zbl 1519.35061 Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Rouleux, M. 2 2023 Global asymptotics for functions of parabolic cylinder and solutions of the Schrödinger equation with a potential in the form of a nonsmooth double well. Zbl 1522.81078 Dobrokhotov, S. Yu.; Tsvetkova, A. V. 1 2023 Asymptotic solutions of the Cauchy problem for the nonlinear shallow water equations in a basin with a gently sloping beach. Zbl 1490.76035 Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E. 3 2022 Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for 2D standing coastal waves. Zbl 1485.35307 Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 2 2022 On expansions in the exact and asymptotic eigenfunctions of the one-dimensional Schrödinger operator. Zbl 1517.81051 Anikin, A. Yu.; Dobrokhotov, S. Yu.; Shkalikov, A. A. 1 2022 Plancherel-Rotach type asymptotic formulae for multiple orthogonal Hermite polynomials and recurrence relations. Zbl 1510.33008 Aptekarev, Alexander I.; Dobrokhotov, Sergey Yu.; Tulyakov, Dmitrii N.; Tsvetkova, Anna V. 1 2022 Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations. Zbl 1492.81056 Dobrokhotov, Sergey Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I. 10 2021 Canonical operator on punctured Lagrangian manifolds. Zbl 1462.35480 Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Schafarevich, A. I. 3 2021 Homogenization of the Cauchy problem for the wave equation with rapidly varying coefficients and initial conditions. Zbl 1501.35031 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 3 2021 An approach to finding the asymptotics of polynomials given by recurrence relations. Zbl 1467.42041 Dobrokhotov, S. Yu.; Tsvetkova, A. V. 3 2021 Representation of Bessel functions by the Maslov canonical operator. Zbl 1471.81033 Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E. 3 2021 Igor’ Moiseevich Krichever. Zbl 1489.01018 Buchstaber, V. M.; Varchenko, A. N.; Veselov, A. P.; Grinevich, P. G.; Grushevsky, S. M.; Dobrokhotov, S. Yu.; Zabrodin, A. V.; Marshakov, A. V.; Mironov, A. E.; Nekrasov, N. A.; Novikov, S. P.; Okounkov, A. Yu.; Olshanetsky, M. A.; Pogrebkov, A. K.; Taimanov, I. A.; Tsfasman, M. A.; Chekhov, L. O.; Sheinman, O. K.; Shlosman, S. B. 1 2021 Lagrangian manifolds and efficient short-wave asymptotics in a neighborhood of a caustic cusp. Zbl 1483.53094 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 8 2020 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. 8 2020 Uniformization of equations with Bessel-type boundary degeneration and semiclassical asymptotics. Zbl 1455.76019 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 5 2020 Airy functions and transition between semiclassical and harmonic oscillator approximations for one-dimensional bound states. Zbl 1453.81024 Anikin, A. Yu.; Dobrokhotov, S. Yu.; Tsvetkova, A. V. 4 2020 Efficient asymptotics in problems on the propagation of waves generated by localized sources in linear multidimensional inhomogeneous and dispersive media. Zbl 1450.35119 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 2 2020 Diophantine tori and pragmatic calculation of quasimodes for operators with integrable principal symbol. Zbl 1452.37071 Anikin, A. Yu.; Dobrokhotov, S. Yu. 2 2020 Variational method for computing ray trajectories and fronts of tsunami waves generated by a localized source. Zbl 1450.35257 Dobrokhotov, S. Yu.; Klimenko, M. V.; Nosikov, I. A.; Tolchennikov, A. A. 1 2020 Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems. Zbl 1441.81091 Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 21 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. 5 2019 Nonstandard Lagrangian singularities and asymptotic eigenfunctions of the degenerating operator \(- \frac{d}{dx}D (x)\frac{d}{dx}\). Zbl 1452.34085 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 4 2019 Asymptotic solution of the Helmholtz equation in a three-dimensional layer of variable thickness with a localized right-hand side. Zbl 1433.35019 Petrov, P. N.; Dobrokhotov, S. Yu. 3 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. 3 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 1418.37094 Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 3 2019 Averaging and spectral bands for the 2-D magnetic Schrödinger operator with growing and one-direction periodic potential. Zbl 1426.81034 Anikin, A. Yu.; Brüning, J.; Dobrokhotov, S. Yu.; Vybornyi, E. V. 2 2019 Classical and quantum dynamics of a particle in a narrow angle. Zbl 1434.35135 Dobrokhotov, Sergei Yu.; Minenkov, Dmitrii S.; Neishtadt, Anatoly I.; Shlosman, Semen B. 2 2019 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. 15 2018 Lagrangian manifolds related to the asymptotics of Hermite polynomials. Zbl 1409.42019 Dobrokhotov, S. Yu.; Tsvetkova, A. V. 12 2018 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. 8 2018 Efficient formulas for the Maslov canonical operator near a simple caustic. Zbl 1406.81036 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 8 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. 7 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. 3 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. 2 2018 One approach to the computation of asymptotics of integrals of rapidly varying functions. Zbl 1397.42004 Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, Anna V. 1 2018 Influence of the elastic base of a basin on the propagation of waves on the water surface. Zbl 1432.76059 Dobrokhotov, S. Yu.; Tolstova, O. L.; Sekerzh-Zenkovich, S. Ya.; Vargas, C. A. 1 2018 New integral representations of the Maslov canonical operator in singular charts. Zbl 1369.81033 Dobrokhotov, Sergei Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I. 26 2017 Punctured Lagrangian manifolds and asymptotic solutions of the linear water wave equations with localized initial conditions. Zbl 1516.35040 Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 21 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. 9 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. 8 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. 8 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. 7 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. 5 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. 5 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. 3 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. 1 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. 8 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. 7 2016 Volume and entropy in abstract analytic number theory and thermodynamics. Zbl 1362.82025 Maslov, V. P.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 4 2016 Maslov’s canonical operator in arbitrary coordinates on the Lagrangian manifold. Zbl 1345.53083 Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Shafarevich, A. I. 4 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 2 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. 2 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. 2 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. 2 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. 1 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. 15 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. 7 2015 On a homogenization method for differential operators with oscillating coefficients. Zbl 1326.35022 Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 6 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. 9 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. 7 2014 Asymptotics of shallow water equations on the sphere. Zbl 1311.76012 Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A. 4 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. 3 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. 2 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. 22 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. 13 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. 12 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. 7 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. 7 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 5 2013 Splitting of lower energy levels in a quantum double well in a magnetic field and tunneling of wave packets in nanowires. Zbl 1286.81057 Brüning, 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 1276.76011 Dobrokhotov, S. Yu.; Lozhnikov, D. A.; Vargas, C. A. 3 2013 Averaging of linear operators, adiabatic approximation, and pseudodifferential operators. Zbl 1282.47079 Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu. 12 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. 5 2012 Asymptotic solutions of the linear shallow-water equations with localized initial data. Zbl 1325.76036 Dobrokhotov, 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 1242.37042 Dobrokhotov, Sergey; Rouleux, Michel 8 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. 6 2011 Generalized Foldy-Wouthuysen transformation and pseudodifferential operators. Zbl 1274.81069 Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya. 4 2011 Remark on the phase shift in the Kuzmak-Whitham ansatz. Zbl 1274.35356 Dobrokhotov, 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 1251.35099 Brüning, 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 1326.35114 Brüning, 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 1387.35404 Dobrokhotov, 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 1196.35161 Dobrokhotov, S. Yu; Tirozzi, B. 16 2010 A class of exact algebraic localized solutions of the multidimensional wave equation. Zbl 1234.35142 Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya. 11 2010 The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory. Zbl 1200.53072 Dobrokhotov, S. Yu.; Rouleux, M. 9 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. 6 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. 5 2010 Peierls substitution and the Maslov operator method. Zbl 1197.35086 Grushin, 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 1178.35301 Dobrokhotov, S. Yu.; Tirozzi, B.; Vargas, C. A. 17 2009 Quantum dynamics in a thin film. II: Stationary states. Zbl 1182.81038 Brüning, 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 1180.35336 Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B. 48 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. 5 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. 4 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. 3 2008 Representations of rapidly decaying functions by the Maslov canonical operator. Zbl 1344.58014 Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 30 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. 11 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. 37 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. 13 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. 11 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. 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 1113.81031 Brüning, J.; Dobrokhotov, S.; Sekerzh-Zenkovich, S.; Tudorovskiy, T. 1 2006 ...and 72 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 296 Authors 109 Dobrokhotov, Sergei Yurievich 47 Nazaikinskii, Vladimir E. 37 Shafarevich, Andreĭ Igorevich 23 Anikin, A. Yu. 20 Tirozzi, Brunello 18 Tolchennikov, Anton A. 18 Tsvetkova, Anna V. 16 Maslov, Viktor Pavlovich 16 Sergeev, Sergeĭ Alekseevich 15 Allilueva, Anna I. 14 Grushin, V. V. 13 Minenkov, Dmitrii S. 12 Brüning, Jochen 12 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 9 Klevin, A. I. 9 Vybornyi, E. V. 7 Rabinovich, Vladimir Samuilovich 6 Kalyakin, Leonid Anatol’evich 6 Vorob’ev, Yu. M. 5 Bulatov, Vitaliĭ Vasil’evich 5 Helffer, Bernard 5 Karasev, Mikhail Vladimirovich 5 Kucherenko, Valeri V. 5 Miller, Peter D. 5 Zhevandrov, Peter N. 4 Belov, Vladimir Vasilyevich 4 Borisov, Denis Ivanovich 4 Lozhnikov, D. A. 4 Mal’tsev, Andreĭ Yakovlevich 4 Nekrasov, R. V. 4 Pelinovsky, Efim 4 Petrov, Pavel S. 4 Sultanov, Oskar A. 4 Topalov, Peter J. 4 Tudorovskii, T. Ya. 3 Aida, Shigeki 3 Brandolese, Lorenzo 3 Fedotov, Alexander 3 Katsnelson, Mikhail I. 3 Kordyukov, Yuri A. 3 Kryvko, Andriy 3 Kuksin, Sergeĭ B. 3 Pereskokov, A. V. 3 Rouleux, Michel 3 Tolstova, O. L. 3 Vargas, Carlos A. 3 Vladimirov, I. Yu. 3 Volkov, B. I. 3 Wilkening, Jon A. 2 Aksenov, Alexander V. 2 Babich, Vasiliĭ Mikhaĭlovich 2 Bikbaev, Ramil’ F. 2 Brezhnev, Yurii V. 2 Chang, Tongkeun 2 Chernyshev, Vsevolod L. 2 Chirkunov, Yuriĭ Aleksandrovich 2 Dell’Antonio, Gian Fausto 2 Dubrovin, Boris Anatol’evich 2 El, Gennady A. 2 Gaydukov, R. K. 2 Haberman, Richard 2 Hu, Chinkun 2 Jin, Bumja 2 Kabanikhin, Sergeĭ Igorevich 2 Khusnutdinova, Karima Robertovna 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 Nosikov, I. A. 2 Novikova, E. M. 2 Pankrashkin, Konstantin 2 Pankratova, T. F. 2 Perel, Maria V. 2 Petrov, P. N. 2 Qin, Yuming 2 Rodríguez Bermúdez, Panters 2 Rodríguez, M. I. Romero 2 Rozanova, Olga S. 2 Rybkin, Alexei 2 Smyth, Noel Frederick 2 Valiño Alonso, Baldomero 2 Vereschagin, Vadim L. 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 Alharthi, N. 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