Edit Profile (opens in new tab) Anikin, A. Yu. Co-Author Distance Author ID: anikin.a-yu Published as: Anikin, A. Yu. Documents Indexed: 27 Publications since 2008 Co-Authors: 15 Co-Authors with 22 Joint Publications 413 Co-Co-Authors all top 5 Co-Authors 5 single-authored 18 Dobrokhotov, Sergei Yurievich 8 Nazaikinskii, Vladimir E. 5 Tsvetkova, Anna V. 3 Klevin, A. I. 2 Brüning, Jochen 2 Rouleux, Michel 2 Tirozzi, Brunello 1 Katsnelson, Mikhail I. 1 Minenkov, Dmitrii S. 1 Nosikov, I. A. 1 Rykhlov, V. V. 1 Shkalikov, Andreĭ Andreevich 1 Tolchennikov, Anton A. 1 Vavilova, M. A. 1 Vybornyi, E. V. all top 5 Serials 11 Theoretical and Mathematical Physics 7 Mathematical Notes 3 Russian Journal of Mathematical Physics 2 Journal of Mathematical Sciences (New York) 1 St. Petersburg Mathematical Journal 1 Doklady Mathematics 1 Regular and Chaotic Dynamics 1 Differential Equations all top 5 Fields 16 Partial differential equations (35-XX) 13 Quantum theory (81-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Ordinary differential equations (34-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Special functions (33-XX) 3 Differential geometry (53-XX) 3 Fluid mechanics (76-XX) 3 Optics, electromagnetic theory (78-XX) 2 Algebraic geometry (14-XX) 2 Mechanics of particles and systems (70-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 21 Publications have been cited 87 times in 56 Documents Cited by ▼ Year ▼ 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 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 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 Asymptotic behavior of the Maupertuis action on a libration and tunneling in a double well. Zbl 1276.81047 Anikin, A. Yu. 7 2013 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 Quantum Birkhoff normal forms. Zbl 1192.81145 Anikin, A. Yu. 4 2009 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 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 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 Normal form of a quantum Hamiltonian with one and a half degrees of freedom near a hyperbolic fixed point. Zbl 1229.81126 Anikin, A. 2 2008 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 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 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 Diophantine tori and pragmatic calculation of quasimodes for operators with integrable principal symbol. Zbl 1452.37071 Anikin, A. Yu.; Dobrokhotov, S. Yu. 2 2020 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 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 Librations and ground-state splitting in a multidimensional double-well problem. Zbl 1286.81054 Anikin, A. Yu. 2 2013 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 Asymptotics of one-dimensional linear standing water waves with dispersion and degeneracy on the boundary. Zbl 1450.76004 Anikin, A. Yu. 1 2020 Semiclassical asymptotic behavior of the lower spectral bands of the Schrödinger operator with a trigonal-symmetric periodic potential. Zbl 1445.81022 Anikin, A. Yu.; Vavilova, M. A. 1 2020 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 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 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 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 Diophantine tori and pragmatic calculation of quasimodes for operators with integrable principal symbol. Zbl 1452.37071 Anikin, A. Yu.; Dobrokhotov, S. Yu. 2 2020 Asymptotics of one-dimensional linear standing water waves with dispersion and degeneracy on the boundary. Zbl 1450.76004 Anikin, A. Yu. 1 2020 Semiclassical asymptotic behavior of the lower spectral bands of the Schrödinger operator with a trigonal-symmetric periodic potential. Zbl 1445.81022 Anikin, A. Yu.; Vavilova, M. 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 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 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 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 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 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 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 Asymptotic behavior of the Maupertuis action on a libration and tunneling in a double well. Zbl 1276.81047 Anikin, A. Yu. 7 2013 Librations and ground-state splitting in a multidimensional double-well problem. Zbl 1286.81054 Anikin, A. Yu. 2 2013 Quantum Birkhoff normal forms. Zbl 1192.81145 Anikin, A. Yu. 4 2009 Normal form of a quantum Hamiltonian with one and a half degrees of freedom near a hyperbolic fixed point. Zbl 1229.81126 Anikin, A. 2 2008 all cited Publications top 5 cited Publications all top 5 Cited by 38 Authors 27 Dobrokhotov, Sergei Yurievich 14 Anikin, A. Yu. 14 Nazaikinskii, Vladimir E. 11 Tsvetkova, Anna V. 5 Klevin, A. I. 5 Minenkov, Dmitrii S. 4 Tolchennikov, Anton A. 3 Novikova, E. M. 2 Katsnelson, Mikhail I. 2 Sergeev, Sergeĭ Alekseevich 2 Vybornyi, E. V. 1 Anikin, Anatoly Y. 1 Aptekarev, Alexander Ivanovich 1 Bogaevskij, Il’ya Aleksandrovich 1 Bova, J. I. 1 Brezhnev, Yurii V. 1 Brüning, Jochen 1 Chernyshev, Vsevolod L. 1 Helffer, Bernard 1 Kuznetsov, Sergey V. 1 Levin, Sergei B. 1 Lukin, Dmitry S. 1 Maslov, Viktor Pavlovich 1 Nekrasov, R. V. 1 Nosikov, I. A. 1 Pankrashkin, Konstantin 1 Petrov, P. N. 1 Reijnders, K. J. A. 1 Rouleux, Michel 1 Rumyantseva, S. V. 1 Rykhlov, V. V. 1 Shafarevich, Andreĭ Igorevich 1 Shkalikov, Andreĭ Andreevich 1 Tirozzi, Brunello 1 Tulyakov, Dmitrii N. 1 Vavilova, M. A. 1 Votiakova, M. M. 1 Zhevandrov, Peter N. all top 5 Cited in 16 Serials 17 Russian Journal of Mathematical Physics 11 Theoretical and Mathematical Physics 10 Mathematical Notes 3 Proceedings of the Steklov Institute of Mathematics 2 Journal of Mathematical Sciences (New York) 2 Differential Equations 1 Russian Mathematical Surveys 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Functional Analysis and its Applications 1 Journal of the London Mathematical Society. Second Series 1 Physica D 1 Asymptotic Analysis 1 Computational Mathematics and Mathematical Physics 1 Annals of Physics 1 St. Petersburg Mathematical Journal 1 Izvestiya: Mathematics all top 5 Cited in 23 Fields 36 Partial differential equations (35-XX) 26 Quantum theory (81-XX) 11 Special functions (33-XX) 9 Fluid mechanics (76-XX) 7 Differential geometry (53-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Ordinary differential equations (34-XX) 5 Optics, electromagnetic theory (78-XX) 4 Algebraic geometry (14-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Difference and functional equations (39-XX) 3 Operator theory (47-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Mechanics of particles and systems (70-XX) 3 Geophysics (86-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Manifolds and cell complexes (57-XX) 1 Combinatorics (05-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Mechanics of deformable solids (74-XX) Citations by Year