Dobrokhotov, Sergey Yu.; Levin, Sergei B.; Tolchennikov, Anton A. Keplerian orbits and global asymptotic solution in the form of an Airy function for the scattering problem on a repulsive Coulomb potential. (English. Russian original) Zbl 07794509 Russ. Math. Surv. 78, No. 4, 788-790 (2023); translation from Usp. Mat. Nauk 78, No. 4, 205-206 (2023). MSC: 81Qxx 33C10 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. Math. Surv. 78, No. 4, 788--790 (2023; Zbl 07794509); translation from Usp. Mat. Nauk 78, No. 4, 205--206 (2023) Full Text: DOI MNR
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. Uniformization and semiclassical asymptotics for a class of equations degenerating on the boundary of a manifold. (English. Russian original) Zbl 1512.35066 J. Math. Sci., New York 270, No. 4, 507-530 (2023); translation from Probl. Mat. Anal. 122, 5-24 (2023). MSC: 35B40 53D12 76B15 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., J. Math. Sci., New York 270, No. 4, 507--530 (2023; Zbl 1512.35066); translation from Probl. Mat. Anal. 122, 5--24 (2023) Full Text: DOI
Nazaikinskii, V. E.; Tolchennikov, A. A. Constructive implementation of semiclassical asymptotic formulas in a neighborhood of a generic caustic cusp. (English) Zbl 1514.53119 Russ. J. Math. Phys. 29, No. 4, 558-567 (2022). MSC: 53D12 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii} and \textit{A. A. Tolchennikov}, Russ. J. Math. Phys. 29, No. 4, 558--567 (2022; Zbl 1514.53119) Full Text: DOI
Dobrokhotov, S. Yu.; Tolchennikov, A. A. Keplerian trajectories and an asymptotic solution of the Schrödinger equation with repulsive Coulomb potential and localized right-hand side. (English) Zbl 1514.35125 Russ. J. Math. Phys. 29, No. 4, 456-466 (2022). MSC: 35J10 35B40 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{A. A. Tolchennikov}, Russ. J. Math. Phys. 29, No. 4, 456--466 (2022; Zbl 1514.35125) Full Text: DOI
Tolchennikov, A. A. On the effect of intersection of characteristics in a two-dimensional massless Dirac equation with linear potential and localized initial condition. (English) Zbl 1469.82046 Russ. J. Math. Phys. 28, No. 2, 265-269 (2021). MSC: 82D80 35Q41 42A38 PDFBibTeX XMLCite \textit{A. A. Tolchennikov}, Russ. J. Math. Phys. 28, No. 2, 265--269 (2021; Zbl 1469.82046) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. Uniform formulas for the asymptotic solution of a linear pseudodifferential equation describing water waves generated by a localized source. (English) Zbl 1448.35391 Russ. J. Math. Phys. 27, No. 2, 185-191 (2020). MSC: 35Q35 35S10 76B15 86A05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 27, No. 2, 185--191 (2020; Zbl 1448.35391) Full Text: DOI
Tolchennikov, A. A. Behavior of the solution of the Klein-Gordon equation with a localized initial condition. (English. Russian original) Zbl 1431.81054 Theor. Math. Phys. 199, No. 2, 761-770 (2019); translation from Teor. Mat. Fiz. 199, No. 2, 330-340 (2019). MSC: 81Q05 81R20 35G10 PDFBibTeX XMLCite \textit{A. A. Tolchennikov}, Theor. Math. Phys. 199, No. 2, 761--770 (2019; Zbl 1431.81054); translation from Teor. Mat. Fiz. 199, No. 2, 330--340 (2019) Full Text: DOI
Dobrokhotov, S. Yu.; Tolchennikov, A. A. Solution of the two-dimensional Dirac equation with a linear potential and a localized initial condition. (English) Zbl 1417.81126 Russ. J. Math. Phys. 26, No. 2, 139-151 (2019). MSC: 81Q05 35F10 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{A. A. Tolchennikov}, Russ. J. Math. Phys. 26, No. 2, 139--151 (2019; Zbl 1417.81126) Full Text: DOI
Tolchennikov, A. A. Simple exact solutions and asymptotic localized solutions of the two-dimensional massless Dirac equation for graphene. (English. Russian original) Zbl 1401.82065 Theor. Math. Phys. 196, No. 1, 996-1001 (2018); translation from Teor. Mat. Fiz. 196, No. 1, 64-69 (2018). MSC: 82D80 81Q05 81U05 PDFBibTeX XMLCite \textit{A. A. Tolchennikov}, Theor. Math. Phys. 196, No. 1, 996--1001 (2018; Zbl 1401.82065); translation from Teor. Mat. Fiz. 196, No. 1, 64--69 (2018) Full Text: DOI
Petrov, P. S.; Sergeev, S. A.; Tolchennikov, A. A. Modeling of pulse signals in 3D propagation problems of deep-water acoustics based on the modified Maslov’s canonical operator. (English) Zbl 1391.76695 Russ. J. Math. Phys. 25, No. 1, 102-112 (2018). MSC: 76Q05 60G35 PDFBibTeX XMLCite \textit{P. S. Petrov} et al., Russ. J. Math. Phys. 25, No. 1, 102--112 (2018; Zbl 1391.76695) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. Asymptotics of linear water waves generated by a localized source near the focal points on the leading edge. (English) Zbl 1432.76203 Russ. J. Math. Phys. 24, No. 4, 544-552 (2017). MSC: 76M35 76B15 86A05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 24, No. 4, 544--552 (2017; Zbl 1432.76203) Full Text: DOI
Dobrokhotov, S. Yu.; Sekerzh-Zen’kovich, S. Ya.; Tolchennikov, A. A. Exact and asymptotic solutions of the Cauchy-Poisson problem with localized initial conditions and a constant function of the bottom. (English) Zbl 1386.76082 Russ. J. Math. Phys. 24, No. 3, 310-321 (2017). MSC: 76E20 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 24, No. 3, 310--321 (2017; Zbl 1386.76082) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. Uniform asymptotics of the boundary values of the solution in a linear problem on the run-up of waves on a shallow beach. (English. Russian original) Zbl 1372.35180 Math. Notes 101, No. 5, 802-814 (2017); translation from Mat. Zametki 101, No. 5, 700-715 (2017). MSC: 35L20 76E20 86A05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Math. Notes 101, No. 5, 802--814 (2017; Zbl 1372.35180); translation from Mat. Zametki 101, No. 5, 700--715 (2017) Full Text: DOI
Petrov, P. S.; Sergeev, S. A.; Tolchennikov, A. A. Modeling of acoustic pulse signal propagation in deep sea using the Maslov canonical operator. (English. Russian original) Zbl 1431.76113 Dokl. Math. 95, No. 2, 181-184 (2017); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 473, No. 2, 142-145 (2017). MSC: 76Q05 35L15 PDFBibTeX XMLCite \textit{P. S. Petrov} et al., Dokl. Math. 95, No. 2, 181--184 (2017; Zbl 1431.76113); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 473, No. 2, 142--145 (2017) Full Text: DOI
Chernyshev, V. L.; Tolchennikov, A. A. Asymptotic estimate for the counting problems corresponding to the dynamical system on some decorated graphs. (English) Zbl 1397.37046 Ergodic Theory Dyn. Syst. 38, No. 5, 1697-1708 (2018). MSC: 37E25 05C90 PDFBibTeX XMLCite \textit{V. L. Chernyshev} and \textit{A. A. Tolchennikov}, Ergodic Theory Dyn. Syst. 38, No. 5, 1697--1708 (2016; Zbl 1397.37046) Full Text: DOI
Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A. Asymptotics of shallow water equations on the sphere. (English) Zbl 1311.76012 Russ. J. Math. Phys. 21, No. 4, 430-449 (2014). MSC: 76B15 35Q35 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 21, No. 4, 430--449 (2014; Zbl 1311.76012) Full Text: DOI