Edit Profile (opens in new tab) Tolchennikov, Anton A. Co-Author Distance Author ID: tolchennikov.anton-a Published as: Tolchennikov, A. A.; Tolchennikov, Anton A.; Tolchennikov, Anton more...less External Links: ORCID Documents Indexed: 34 Publications since 2008, including 4 Additional arXiv Preprints Co-Authors: 13 Co-Authors with 27 Joint Publications 388 Co-Co-Authors all top 5 Co-Authors 7 single-authored 12 Chernyshev, Vsevolod L. 10 Dobrokhotov, Sergei Yurievich 5 Nazaikinskii, Vladimir E. 3 Sergeev, Sergeĭ Alekseevich 2 Petrov, Pavel S. 2 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 1 Anikin, A. Yu. 1 Klimenko, M. V. 1 Levin, Sergei B. 1 Minenkov, Dmitrii S. 1 Nosikov, I. A. 1 Shafarevich, Andreĭ Igorevich 1 Tirozzi, Brunello all top 5 Serials 16 Russian Journal of Mathematical Physics 3 Theoretical and Mathematical Physics 2 Mathematical Notes 2 Regular and Chaotic Dynamics 1 Russian Mathematical Surveys 1 Ergodic Theory and Dynamical Systems 1 Computational Mathematics and Mathematical Physics 1 Journal of Mathematical Sciences (New York) 1 Sbornik: Mathematics 1 Doklady Mathematics all top 5 Fields 14 Partial differential equations (35-XX) 11 Fluid mechanics (76-XX) 9 Combinatorics (05-XX) 8 Quantum theory (81-XX) 5 Geophysics (86-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Number theory (11-XX) 3 Operator theory (47-XX) 3 Differential geometry (53-XX) 2 Potential theory (31-XX) 2 Manifolds and cell complexes (57-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 21 Publications have been cited 79 times in 52 Documents Cited by ▼ Year ▼ Correction to the leading term of asymptotics in the problem of counting the number of points moving on a metric tree. Zbl 1377.05027 Chernyshev, V. L.; Tolchennikov, A. A. 9 2017 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 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 The second term in the asymptotics for the number of points moving along a metric graph. Zbl 1416.11141 Chernyshev, Vsevolod L.; Tolchennikov, Anton A. 6 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 Behavior of quasi-particles on hybrid spaces. Relations to the geometry of geodesics and to the problems of analytic number theory. Zbl 1353.37140 Chernyshev, Vsevolod L.; Tolchennikov, Anton A.; Shafarevich, Andrei I. 5 2016 Polynomial approximation for the number of all possible endpoints of a random walk on a metric graph. Zbl 1460.05178 Chernyshev, Vsevolod; Tolchennikov, Anton 5 2018 Asymptotic estimate for the counting problems corresponding to the dynamical system on some decorated graphs. Zbl 1397.37046 Chernyshev, V. L.; Tolchennikov, A. A. 5 2016 Asymptotics of shallow water equations on the sphere. Zbl 1311.76012 Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A. 4 2014 The kernel of Laplace-Beltrami operators with zero-radius potential or on decorated graphs. Zbl 1268.47058 Tolchennikov, A. A. 4 2008 Creation operators in the problem of localized solutions of the linearized shallow water equations with regular and singular characteristics. Zbl 1362.35242 Sergeev, S. A.; Tolchennikov, A. A. 3 2016 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 The number of endpoints of a random walk on a semi-infinite metric path graph. Zbl 1467.05248 Chernyshev, V. L.; Minenkov, D. S.; Tolchennikov, A. A. 2 2021 Simple exact solutions and asymptotic localized solutions of the two-dimensional massless Dirac equation for graphene. Zbl 1401.82065 Tolchennikov, A. A. 2 2018 Kernel and trace formula for the exponential of the Laplace-Beltrami operator on a decorated graph. Zbl 1177.31005 Tolchennikov, A. A. 1 2008 Modeling of acoustic pulse signal propagation in deep sea using the Maslov canonical operator. Zbl 1431.76113 Petrov, P. S.; Sergeev, S. A.; Tolchennikov, A. A. 1 2017 Asymptotics of the number of endpoints of a random walk on a certain class of directed metric graphs. Zbl 1479.05328 Chernyshev, V. L.; Tolchennikov, A. A. 1 2021 Behavior of the solution of the Klein-Gordon equation with a localized initial condition. Zbl 1431.81054 Tolchennikov, A. A. 1 2019 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 Asymptotics of the trace of the resolvent of the Laplace operator on a metric graph with arbitrary boundary conditions. Zbl 1417.81132 Tolchennikov, A. A. 1 2019 The number of endpoints of a random walk on a semi-infinite metric path graph. Zbl 1467.05248 Chernyshev, V. L.; Minenkov, D. S.; Tolchennikov, A. A. 2 2021 Asymptotics of the number of endpoints of a random walk on a certain class of directed metric graphs. Zbl 1479.05328 Chernyshev, V. L.; Tolchennikov, A. A. 1 2021 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 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 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 Behavior of the solution of the Klein-Gordon equation with a localized initial condition. Zbl 1431.81054 Tolchennikov, A. A. 1 2019 Asymptotics of the trace of the resolvent of the Laplace operator on a metric graph with arbitrary boundary conditions. Zbl 1417.81132 Tolchennikov, A. A. 1 2019 Polynomial approximation for the number of all possible endpoints of a random walk on a metric graph. Zbl 1460.05178 Chernyshev, Vsevolod; Tolchennikov, Anton 5 2018 Simple exact solutions and asymptotic localized solutions of the two-dimensional massless Dirac equation for graphene. Zbl 1401.82065 Tolchennikov, A. A. 2 2018 Correction to the leading term of asymptotics in the problem of counting the number of points moving on a metric tree. Zbl 1377.05027 Chernyshev, V. L.; Tolchennikov, A. A. 9 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 The second term in the asymptotics for the number of points moving along a metric graph. Zbl 1416.11141 Chernyshev, Vsevolod L.; Tolchennikov, Anton A. 6 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 Modeling of acoustic pulse signal propagation in deep sea using the Maslov canonical operator. Zbl 1431.76113 Petrov, P. S.; Sergeev, S. A.; Tolchennikov, A. A. 1 2017 Behavior of quasi-particles on hybrid spaces. Relations to the geometry of geodesics and to the problems of analytic number theory. Zbl 1353.37140 Chernyshev, Vsevolod L.; Tolchennikov, Anton A.; Shafarevich, Andrei I. 5 2016 Asymptotic estimate for the counting problems corresponding to the dynamical system on some decorated graphs. Zbl 1397.37046 Chernyshev, V. L.; Tolchennikov, A. A. 5 2016 Creation operators in the problem of localized solutions of the linearized shallow water equations with regular and singular characteristics. Zbl 1362.35242 Sergeev, S. A.; Tolchennikov, A. A. 3 2016 Asymptotics of shallow water equations on the sphere. Zbl 1311.76012 Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A. 4 2014 The kernel of Laplace-Beltrami operators with zero-radius potential or on decorated graphs. Zbl 1268.47058 Tolchennikov, A. A. 4 2008 Kernel and trace formula for the exponential of the Laplace-Beltrami operator on a decorated graph. Zbl 1177.31005 Tolchennikov, A. A. 1 2008 all cited Publications top 5 cited Publications all top 5 Cited by 33 Authors 18 Tolchennikov, Anton A. 17 Dobrokhotov, Sergei Yurievich 16 Nazaikinskii, Vladimir E. 11 Chernyshev, Vsevolod L. 6 Minenkov, Dmitrii S. 4 Anikin, A. Yu. 4 Shafarevich, Andreĭ Igorevich 4 Tsvetkova, Anna V. 3 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 3 Sergeev, Sergeĭ Alekseevich 1 Bogaevskij, Il’ya Aleksandrovich 1 Bova, J. I. 1 Dombrovskaya, Zh. O. 1 Grushin, V. V. 1 Hilberdink, Titus W. 1 Lozhnikov, D. A. 1 Lukin, Dmitry S. 1 Palmer, Noah 1 Pankrashkin, Konstantin 1 Pelinovsky, Efim 1 Petrov, Pavel S. 1 Pyat’ko, D. V. 1 Roganova, Svetlana 1 Rybkin, Alexei 1 Sakbaev, Vsevolod Zhanovich 1 Schafarevich, A. I. 1 Smirnova, Elena S. 1 Tolstova, O. L. 1 Vakhitov, Murat V. 1 Vargas, Carlos A. 1 Volovich, Igor’ Vasil’evich 1 Yeganefar, Nader 1 Zhevandrov, Peter N. all top 5 Cited in 15 Serials 21 Russian Journal of Mathematical Physics 9 Mathematical Notes 4 Theoretical and Mathematical Physics 2 Functional Analysis and its Applications 2 Computational Mathematics and Mathematical Physics 2 Regular and Chaotic Dynamics 2 Proceedings of the Steklov Institute of Mathematics 1 Journal of Applied Mathematics and Mechanics 1 Integral Equations and Operator Theory 1 Applied Mathematics Letters 1 Journal of Mathematical Sciences (New York) 1 Doklady Mathematics 1 Matematicheskoe Modelirovanie 1 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 1 Moscow Journal of Combinatorics and Number Theory all top 5 Cited in 23 Fields 22 Partial differential equations (35-XX) 16 Fluid mechanics (76-XX) 9 Quantum theory (81-XX) 8 Combinatorics (05-XX) 8 Geophysics (86-XX) 7 Differential geometry (53-XX) 5 Number theory (11-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Operator theory (47-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Optics, electromagnetic theory (78-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Ordinary differential equations (34-XX) 2 Approximations and expansions (41-XX) 2 Probability theory and stochastic processes (60-XX) 2 Numerical analysis (65-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year