M. A. Nikulin, Th. Yu. Popelensky, A. I. Shafarevich, “Asymptotic behaviour of energy levels of a quantum free particle in an elliptic sector”, Phys. Scr., 99:1 (2024), 015207 ;
2.
V. V. Rykhlov, A. I. Shafarevich, “Spectral Series of the Schrödinger Operator with Double Delta Potential on Two- and Three-Dimensional Surfaces of Revolution”, Mat. Zametki, 116:6 (2024) (to appear)
3.
A. I. Shafarevich, O. A. Shchegortsova, “Reconstruction of Maslov's complex germ in the Cauchy problem for the Schrödinger equation with a delta potential localized on a hypersurface”, Russ. J. Math. Phys., 31:3 (2024), 526–543;
4.
A. I. Alillueva, A. I. Shafarevich, “Quasi-classical asymptotics describing the electron-hole interaction and the Klein effect for the (2+1)-Dirac equation in abruptly varying fields”, Russ. J. Math. Phys., 31:3 (2024), 339–350;
2023
5.
V. V. Aleksandrov, D. V. Georgievskii, V. P. Karlikov, S. S. Lemak, G. V. Moskvitin, R. I. Nigmatulin, V. A. Sadovnichii, S. L. Tolokonnikov, V. N. Chubarikov, A. I. Shafarevich, V. Ya. Shkadov, “To hundred anniversary of Viktor Vasil’evich Moskvitin”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023, no. 5, 70–71
2022
6.
S. A. Stepin, A. I. Shafarevich, “WKB method for nonlinear equations of Emden–Fowler type”, Dokl. Math., 105:1 (2022), 39–44
7.
A. I. Shafarevich, O. A. Shchegortsova, “Maslov complex germ and semiclassical contracted states in the Cauchy problem for the Schrödinger equation with delta potential”, Differential and functional differential equations, CMFD, 68, no. 4, PFUR, M., 2022, 704–715
2021
8.
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations”, Russian Math. Surveys, 76:5 (2021), 745–819
9.
A. V. Tsvetkova, A. I. Shafarevich, “The wave equation with symmetric velocity on the hybrid manifold obtained by gluing a ray to a three-dimensional sphere”, Trans. Moscow Math. Soc., 82 (2021), 305–325
2020
10.
A. V. Tsvetkova, A. I. Shafarevich, “Localized Asymptotic Solution of a Variable-Velocity Wave Equation on the Simplest Decorated Graph with Initial Conditions on a Surface”, Math. Notes, 108:4 (2020), 590–602
11.
A. V. Tsvetkova, A. I. Shafarevich, “Asymptotics of the Solution of a Wave Equation with Radially Symmetric Velocity on the Simplest Decorated Graph with Arbitrary Boundary Conditions at the Gluing Point”, Math. Notes, 107:3 (2020), 478–487
12.
A. I. Shafarevich, O. A. Shchegortsova, “Semiclassical Asymptotics of the Solution to the Cauchy Problem for the Schrödinger Equation with a Delta Potential Localized on a Codimension 1 Surface”, Proc. Steklov Inst. Math., 310 (2020), 304–313
13.
A. V. Tsvetkova, A. I. Shafarevich, “Localized Asymptotic Solution of a Variable-Velocity Wave Equation on the Simplest Decorated Graph”, Proc. Steklov Inst. Math., 308 (2020), 250–260
2019
14.
V. E. Nazaikinskii, A. I. Shafarevich, “Maslov's Canonical Operator in Problems on Localized Asymptotic Solutions of Hyperbolic Equations and Systems”, Math. Notes, 106:3 (2019), 402–411
15.
Anna I. Allilueva, Andrei I. Shafarevich, “Conic Lagrangian Varieties and Localized Asymptotic Solutions of Linearized Equations of Relativistic Gas Dynamics”, Regul. Chaotic Dyn., 24:6 (2019), 671–681;
16.
Anna I. Allilueva, Andrei I. Shafarevich, “Evolution of Lagrangian Manifolds and Asymptotic Solutions to the Linearized Equations of Gas Dynamics”, Regul. Chaotic Dyn., 24:1 (2019), 80–89;
A. I. Shafarevich, “Lagrangian Tori and Quantization Conditions Corresponding to Spectral Series of the Laplace Operator on a Surface of Revolution with Conical Points”, Proc. Steklov Inst. Math., 307 (2019), 294–302
2018
18.
Andrei I. Shafarevich, “The Maslov Complex Germ and Semiclassical Spectral Series Corresponding to Singular Invariant Curves of Partially Integrable Hamiltonian Systems”, Regul. Chaotic Dyn., 23:7-8 (2018), 842–849;
2017
19.
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “New integral representations of the Maslov canonical operator in singular charts”, Izv. Math., 81:2 (2017), 286–328
20.
A. I. Allilueva, A. I. Shafarevich, “Localized Asymptotic Solutions of the Linearized System of Magnetic Hydrodynamics”, Math. Notes, 102:6 (2017), 737–745
21.
D. V. Nekhaev, A. I. Shafarevich, “A quasiclassical limit of the spectrum of a Schrödinger operator with complex periodic potential”, Sb. Math., 208:10 (2017), 1535–1556
22.
A. I. Allilueva, A. I. Shafarevich, “Nonstandard characteristics and localized asymptotic solutions of a linearized magnetohydrodynamic system with small viscosity and drag”, Theoret. and Math. Phys., 190:1 (2017), 164–175
2016
23.
A. V. Tsvetkova, A. I. Shafarevich, “The Cauchy Problem for the Wave Equation on Homogeneous Trees”, Math. Notes, 100:6 (2016), 862–869
24.
A. I. Alillueva, A. I. Shafarevich, “Asymptotic Solutions of a Magnetohydrodynamic System which Describe Smoothed Discontinuities”, Math. Notes, 99:6 (2016), 795–809
25.
Vsevolod L. Chernyshev, Anton A. Tolchennikov, Andrei I. Shafarevich, “Behavior of Quasi-particles on Hybrid Spaces. Relations to the Geometry of Geodesics and to the Problems of Analytic Number Theory”, Regul. Chaotic Dyn., 21:5 (2016), 531–537;
V. P. Maslov, A. I. Shafarevich, “Fomenko invariants in the asymptotic theory of the Navier–Stokes equations”, J. Math. Sci., 225:4 (2017), 666–680
2015
27.
Anna I. Allilueva, Andrei I. Shafarevich, “Asymptotic Solutions for Linear and Nonlinear MHD Systems with a Rapid Jump near a Surface. Dynamics of the Surface of the Jump and Evolution of the Magnetic Field”, Regul. Chaotic Dyn., 20:6 (2015), 691–700;
2014
28.
A. I. Esina, A. I. Shafarevich, “Asymptotics of the Spectrum and Eigenfunctions of the Magnetic Induction Operator on a Compact Two-Dimensional Surface of Revolution”, Math. Notes, 95:3 (2014), 374–387
29.
V. P. Maslov, A. I. Shafarevich, “Asymptotic solutions of Navier–Stokes equations and topological invariants of vector fields and Liouville foliations”, Theoret. and Math. Phys., 180:2 (2014), 967–982
2010
30.
A. I. Esina, A. I. Shafarevich, “Quantization Conditions on Riemannian Surfaces and the Semiclassical Spectrum of the Schrödinger Operator with Complex Potential”, Math. Notes, 88:2 (2010), 209–227
31.
A. A. Tolchennikov, V. L. Chernyshev, A. I. Shafarevich, “Asimptoticheskie svoistva i klassicheskie dinamicheskie sistemy v kvantovykh zadachakh na singulyarnykh prostranstvakh”, Nelineinaya dinam., 6:3 (2010), 623–638;
T. A. Filatova, A. I. Shafarevich, “Semiclassical spectral series of the Schrödinger operator with a delta potential on a straight line and on a sphere”, Theoret. and Math. Phys., 164:2 (2010), 1064–1080
2008
33.
J. Brüning, S. Yu. Dobrokhotov, R. V. Nekrasov, A. I. Shafarevich, “Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity”, Theoret. and Math. Phys., 155:2 (2008), 689–707
2007
34.
S. Yu. Dobrokhotov, B. Tirozzi, A. I. Shafarevich, “Representations of Rapidly Decreasing Functions by the Maslov Canonical Operator”, Math. Notes, 82:5 (2007), 713–717
35.
V. L. Chernyshev, A. I. Shafarevich, “Semiclassical Spectrum of the Schrödinger Operator on a Geometric Graph”, Math. Notes, 82:4 (2007), 542–554
36.
J. Brüning, R. V. Nekrasov, A. I. Shafarevich, “Quantization of Periodic Motions on Compact Surfaces of Constant Negative Curvature in a Magnetic Field”, Math. Notes, 81:1 (2007), 28–36
2006
37.
S. V. Galtsev, A. I. Shafarevich, “Spectrum and Pseudospectrum of non-self-adjoint Schrödinger Operators with Periodic Coefficients”, Math. Notes, 80:3 (2006), 345–354
38.
S. V. Galtsev, A. I. Shafarevich, “Quantized Riemann surfaces and semiclassical spectral series for a non-self-adjoint Schrödinger operator with periodic coefficients”, Theoret. and Math. Phys., 148:2 (2006), 1049–1066
2004
39.
V. P. Maslov, A. I. Shafarevich, “On Asymptotic Solutions of Nonlinear Equations in the Presence of Turning Points”, Differ. Equ., 40:5 (2004), 736–741
2000
40.
S. Yu. Dobrokhotov, A. I. Shafarevich, “Tunnel Splitting of the Spectrum of the Beltrami–Laplace Operators on Two-Dimensional Surfaces with Square Integrable Geodesic Flow”, Funct. Anal. Appl., 34:2 (2000), 133–134
41.
A. I. Shafarevich, “The Navier–Stokes equations: Asymptotic solutions describing tangential discontinuities”, Math. Notes, 67:6 (2000), 792–801
1998
42.
A. I. Shafarevich, “Differential equations on graphs that describe asymptotic solutions of Navier–Stokes equations localized in a small neighborhood of a curve”, Differ. Equ., 34:8 (1998), 1124–1134
1996
43.
V. P. Maslov, A. I. Shafarevich, “Asymptotic laminar solutions of Navier–Stokes equations, localized in a small neighborhood of a curve, and their large-scale perturbations”, Dokl. Math., 41:11 (1996), 540–543
44.
V. P. Maslov, A. I. Shafarevich, “Asymptotic theory of localized solutions of Navier–Stokes equations with small viscosity”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1996, no. 6, 16–18
1995
45.
S. A. Vakulenko, V. P. Maslov, I. A. Molotkov, A. I. Shafarevich, “Asymptotic solutions of the Hartree equation that are concentrated, as $h\to 0$, in a small neighborhood of a curve”, Dokl. Akad. Nauk, 345:6 (1995), 743–745
1994
46.
A. I. Shafarevich, “Behavior of rapidly decreasing asymptotic solutions of linearized Navier–Stokes equations $t\to\infty$”, Math. Notes, 55:6 (1994), 632–647
1993
47.
S. Yu. Dobrokhotov, A. I. Shafarevich, “Some asymptotic solutions of linearized Navier–Stokes equations”, Math. Notes, 53:1 (1993), 19–26
1992
48.
S. Yu. Dobrokhotov, A. I. Shafarevich, “Parametrix and the asymptotics of localized solutions of the Navier-Stokes equations in $\mathbf{R}^3$, linearized on a smooth flow”, Math. Notes, 51:1 (1992), 47–54
1991
49.
S. Yu. Dobrokhotov, P. N. Zhevandrov, V. P. Maslov, A. I. Shafarevich, “Asymptotic fast-decreasing solutions of linear, strictly hyperbolic systems with variable coefficients”, Math. Notes, 49:4 (1991), 355–365
1989
50.
A. I. Shafarevich, “Quasiclassical scattering of wave packets on a narrow band in which the potential rapidly changes”, Math. Notes, 45:1 (1989), 72–77
1987
51.
S. Yu. Dobrokhotov, A. I. Shafarevich, “Quasiclassical asymptotics in the problem of the scattering of wave packets by a rapidly changing potential of the form $-2\vert \nabla\Phi\vert ^2/{\rm ch}^2(\Phi (x)/h)+V_0(x)$”, Dokl. Akad. Nauk SSSR, 295:6 (1987), 1347–1351
Semiclassical asymptotics for equations with singularities A. I. Shafarevich III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 11, 2023 10:55
The current status of the theory of the canonical operator V. P. Maslov, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich International Conference Dedicated to the 100th Anniversary of the Birthday
of V. S. Vladimirov (Vladimirov-100) January 12, 2023 11:00
2024
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