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Found 135 Documents (Results 1–100)

100
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Boltzmann and Poincaré entropy, Boltzmann extremals, and Hamilton-Jacobi method for non-Hamiltonian situation. (English. Russian original) Zbl 07542521

J. Math. Sci., New York 260, No. 4, 434-455 (2022); translation from Sovrem. Mat., Fundam. Napravl. 64, No. 1, 37-59 (2018).
MSC:  82Cxx 37Jxx 70Hxx
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Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for 2D standing coastal waves. (English. Russian original) Zbl 1485.35307

St. Petersbg. Math. J. 33, No. 2, 185-205 (2022); translation from Algebra Anal. 33, No. 2, 5-34 (2021).
MSC:  35P20 35B40 35J25
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Constructive semiclassical asymptotics of bound states of graphene in a constant magnetic field with small mass. (English. Russian original) Zbl 1486.81113

Math. Notes 111, No. 2, 173-192 (2022); translation from Mat. Zametki 111, No. 2, 163-187 (2022).
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On analogs of wave catastrophe functions that are solutions of nonlinear integrable equations. (English. Russian original) Zbl 1475.35015

J. Math. Sci., New York 258, No. 1, 81-96 (2021); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 163, 81-95 (2019).
MSC:  35B06 35Q55
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On the hierarchical behavior of solutions of the Maryland equation in the semiclassical approximation. (English. Russian original) Zbl 1454.81067

Math. Notes 108, No. 6, 906-910 (2020); translation from Mat. Zametki 108, No. 6, 941-946 (2020).
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Semiclassical asymptotics of the solution to the Cauchy problem for the Schrödinger equation with a delta potential localized on a codimension 1 surface. (English. Russian original) Zbl 1455.35213

Proc. Steklov Inst. Math. 310, 304-313 (2020); translation from Tr. Mat. Inst. Steklova 310, 322-331 (2020).
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Localized asymptotic solution of a variable-velocity wave equation on the simplest decorated graph with initial conditions on a surface. (English. Russian original) Zbl 1451.35243

Math. Notes 108, No. 4, 590-602 (2020); translation from Mat. Zametki 108, No. 4, 601-616 (2020).
MSC:  35R02 35L15 35L05
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Lagrangian manifolds and efficient short-wave asymptotics in a neighborhood of a caustic cusp. (English. Russian original) Zbl 1483.53094

Math. Notes 108, No. 3, 318-338 (2020); translation from Mat. Zametki 108, No. 3, 334-359 (2020).
MSC:  53D12 41A60
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Index iteration theories for periodic orbits: old and new. (English) Zbl 1457.37082

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Uniformization of equations with Bessel-type boundary degeneration and semiclassical asymptotics. (English. Russian original) Zbl 1455.76019

Math. Notes 107, No. 5, 847-853 (2020); translation from Mat. Zametki 107, No. 5, 780-786 (2020).
MSC:  76B15 76M45 35Q35
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Asymptotics of the spectrum of the hydrogen atom in orthogonal electric and magnetic fields near the lower boundaries of spectral clusters. (English. Russian original) Zbl 07215589

Math. Notes 107, No. 5, 804-819 (2020); translation from Mat. Zametki 107, No. 5, 734-751 (2020).
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Localized asymptotic solution of a variable-velocity wave equation on the simplest decorated graph. (English. Russian original) Zbl 1440.35205

Proc. Steklov Inst. Math. 308, 250-260 (2020); translation from Tr. Mat. Inst. Steklova 308, 265-275 (2020).
MSC:  35L20 35R02
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Lagrangian tori and quantization conditions corresponding to spectral series of the Laplace operator on a surface of revolution with conical points. (English. Russian original) Zbl 1440.35223

Proc. Steklov Inst. Math. 307, 294-302 (2019); translation from Tr. Mat. Inst. Steklova 307, 319-327 (2019).
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Bateman-Hörmander two-dimensional waves with a singularity at a running point. (English. Russian original) Zbl 1435.35208

Math. Notes 106, No. 5, 845-848 (2019); translation from Mat. Zametki 106, No. 5, 793-796 (2019).
MSC:  35L05 35A21 35C05
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Asymptotic solutions of the Cauchy problem with localized initial data for a finite-difference scheme corresponding to the one-dimensional wave equation. (English. Russian original) Zbl 1436.35337

Math. Notes 106, No. 5, 800-813 (2019); translation from Mat. Zametki 106, No. 5, 744-760 (2019).
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Nonstandard Lagrangian singularities and asymptotic eigenfunctions of the degenerating operator \(- \frac{d}{dx}D (x)\frac{d}{dx}\). (English. Russian original) Zbl 1452.34085

Proc. Steklov Inst. Math. 306, 74-89 (2019); translation from Tr. Mat. Inst. Steklova 306, 83-99 (2019).
MSC:  34L10 34L15
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Maslov’s canonical operator in problems on localized asymptotic solutions of hyperbolic equations and systems. (English. Russian original) Zbl 1432.35025

Math. Notes 106, No. 3, 402-411 (2019); translation from Mat. Zametki 106, No. 3, 424-435 (2019).
MSC:  35B40 58J40 53D12
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Asymptotics, related to billiards with semi-rigid walls, of eigenfunctions of the \(\nabla D(x)\nabla\) operator in dimension 2 and trapped coastal waves. (English. Russian original) Zbl 1426.37049

Math. Notes 105, No. 5, 789-794 (2019); translation from Mat. Zametki 105, No. 5, 792-797 (2019).
MSC:  37J35 37J10 34L10 34L20
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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. (English. Russian original) Zbl 1418.37094

Differ. Equ. 55, No. 5, 644-657 (2019); translation from Differ. Uravn. 55, No. 5, 660-672 (2019).
MSC:  37J35 37J05 37D50 53D12 53D25 35P05
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Simple asymptotics for a generalized wave equation with degenerating velocity and their applications in the linear long wave run-up problem. (English. Russian original) Zbl 1420.35151

Math. Notes 104, No. 4, 471-488 (2018); translation from Mat. Zametki 104, No. 4, 483-504 (2018).
MSC:  35L20 35B40
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Homogenization method in the problem of long wave propagation from a localized source in a basin over an uneven bottom. (English. Russian original) Zbl 1418.76043

Differ. Equ. 54, No. 8, 1057-1072 (2018); translation from Differ. Uravn. 54, No. 8, 1075-1089 (2018).
MSC:  76M50 76B15 76M45
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One approach to the computation of asymptotics of integrals of rapidly varying functions. (English. Russian original) Zbl 1397.42004

Math. Notes 103, No. 5, 713-723 (2018); translation from Mat. Zametki 103, No. 5, 680-692 (2018).
MSC:  42B20 41A60
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Punctured Lagrangian manifolds and asymptotic solutions of the linear water wave equations with localized initial conditions. (English. Russian original) Zbl 06769034

Math. Notes 101, No. 6, 1053-1060 (2017); translation from Mat. Zametki 101, No. 6, 936-942 (2017).
MSC:  35Lxx
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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
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Approximation of solutions of the two-dimensional wave equation with variable velocity and localized right-hand side using some “simple” solutions. (English. Russian original) Zbl 1362.35169

Math. Notes 100, No. 6, 796-806 (2016); translation from Mat. Zametki 100, No. 6, 825-837 (2016).
MSC:  35L20
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Characteristics with singularities and the boundary values of the asymptotic solution of the Cauchy problem for a degenerate wave equation. (English. Russian original) Zbl 1362.35170

Math. Notes 100, No. 5, 695-713 (2016); translation from Mat. Zametki 100, No. 5, 710-731 (2016).
MSC:  35L20 35L80 35B40
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Semiclassical asymptotic approximations and the density of states for the two-dimensional radially symmetric Schrödinger and Dirac equations in tunnel microscopy problems. (English. Russian original) Zbl 1338.81182

Theor. Math. Phys. 186, No. 3, 333-345 (2016); translation from Teor. Mat. Fiz. 186, No. 3, 386-400 (2016).
MSC:  81Q05 81Q20
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New representations of the Maslov canonical operator and localized asymptotic solutions for strictly hyperbolic systems. (English. Russian original) Zbl 1331.35219

Dokl. Math. 92, No. 2, 548-553 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 464, No. 3, 261-266 (2015).
MSC:  35L45 35C20
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The Maupertuis-Jacobi principle for Hamiltonians of the form \(F(x,|p|)\) in two-dimensional stationary semiclassical problems. (English. Russian original) Zbl 1360.37159

Math. Notes 97, No. 1, 42-49 (2015); translation from Mat. Zametki 97, No. 1, 48-57 (2015).
MSC:  37K05 35J10 35Q41
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The Maslov canonical operator on Lagrangian manifolds in the phase space corresponding to a wave equation degenerating on the boundary. (English. Russian original) Zbl 1330.53108

Math. Notes 96, No. 2, 248-260 (2014); translation from Mat. Zametki 96, No. 2, 261-276 (2014).
MSC:  53D12 35L05
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Maslov’s canonical operator, Hörmander’s formula, and localization of the Berry-Balazs solution in the theory of wave beams. (English. Russian original) Zbl 1323.81031

Theor. Math. Phys. 180, No. 2, 894-916 (2014); translation from Teor. Mat. Fiz. 180, No. 2, 162-188 (2014).
MSC:  81Q05 35C05 35Q41
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Short-wave asymptotics of solutions of the Cauchy problem for hyperbolic systems with constant coefficients and with characteristics of variable multiplicity. (English. Russian original) Zbl 1297.35129

Differ. Equ. 50, No. 5, 667-676 (2014); translation from Differ. Uravn. 50, No. 5, 670-679 (2014).
MSC:  35L45 35G20 35Q61
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Estimate of accuracy of solution of the nonlocal Fisher-Kolomogorov-Petrovskii-Piskunov equation. (English. Russian original) Zbl 1298.35023

Russ. Phys. J. 55, No. 12, 1425-1433 (2013); translation from Izv. Vyssh. Uchebn. Zaved., Fiz., No. 12, 47-53 (2012).
MSC:  35B65 35G05 81Q20
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Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source. (English. Russian original) Zbl 1293.35279

Proc. Steklov Inst. Math. 281, 161-178 (2013); translation from Tr. Mat. Inst. Steklova 281, 170-187 (2013); corrigendum Proc. Steklov Inst. Math. 288, 265 (2015); translation from Tr. Mat. Inst. Steklova 288, 287 (2015).
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Averaging of linear operators, adiabatic approximation, and pseudodifferential operators. (English. Russian original) Zbl 1282.47079

Math. Notes 92, No. 2, 151-165 (2012); translation from Mat. Zametki 92, No. 2, 163-180 (2012).
MSC:  47N20 35Q40
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Noncompact Lagrangian manifolds corresponding to the spectral series of the Schrödinger operator with delta-potential on a surface of revolution. (English. Russian original) Zbl 1266.58015

Dokl. Math. 86, No. 2, 694-696 (2012); translation from Dokl. Akad. Nauk. 446, No. 6, 618-620 (2012).
MSC:  58J50 35J10 34E05
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Semiclassical spectral series for the two-component Hartree-type equation. (English. Russian original) Zbl 1257.81028

Russ. Phys. J. 54, No. 6, 639-648 (2011); translation from Izv. Vyssh. Uchebn. Zaved., Fiz., No. 6, 21-29 (2011).
MSC:  81Q20 35Q55 81Q10
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Semiclassical spectral series of the Schrödinger operator with a delta potential on a straight line and on a sphere. (English. Russian original) Zbl 1298.81069

Theor. Math. Phys. 164, No. 2, 1064-1080 (2010); translation from Teor. Mat. Fiz. 164, No. 2, 279-298 (2010).
MSC:  81Q05 81Q20
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The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory. (English. Russian original) Zbl 1200.53072

Math. Notes 87, No. 3, 430-435 (2010); translation from Mat. Zametki 87, No. 3, 458-463 (2010).
MSC:  53D12
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An analog of the Bohr-Sommerfeld quantization rule for geometric graphs. Description of kernels of the Laplace operator. (English. Russian original) Zbl 1185.35306

J. Math. Sci., New York 158, No. 2, 184-198 (2009); translation from Sovrem. Mat. Prilozh. 54 (2008).
MSC:  35R02 35J10 35P20
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On real hyperbolic systems with characteristics of variable multiplicity. (English. Russian original) Zbl 1327.35240

Dokl. Math. 75, No. 1, 83-86 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 412, No. 4, 451-455 (2007).
MSC:  35L60 35Q35 35Q60
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Asymptotic solution of a linear system with a high-order rotation point. (English. Russian original) Zbl 1327.34107

Dokl. Math. 75, No. 1, 58-61 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 412, No. 3, 308-311 (2007).
MSC:  34E20 81Q10 81Q20
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Semiclassical spectrum of the Schrödinger operator on a geometric graph. (English. Russian original) Zbl 1160.47022

Math. Notes 82, No. 4, 542-554 (2007); translation from Mat. Zametki 82, No. 4, 606-620 (2007).
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Fundamental solutions of the equations of quantum mechanics as distributions and distinctive properties of the Dirac equation solutions. (English. Russian original) Zbl 1138.81377

Theor. Math. Phys. 151, No. 2, 681-692 (2007); translation from Teor. Mat. Fiz. 151, No. 2, 287-301 (2007).
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Quantization of periodic motions on compact surfaces of constant negative curvature in a magnetic field. (English. Russian original) Zbl 1132.81033

Math. Notes 81, No. 1, 28-36 (2007); translation from Mat. Zametki 81, No. 1, 32-42 (2006).
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Application of integral equations to finding asymptotics of solutions of singularly perturbed semilinear heat equations. (English. Russian original) Zbl 1131.35302

Differ. Equ. 41, No. 9, 1225-1236 (2005); translation from Differ. Uravn. 41, No. 9, 1166-1176 (2005).
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The effect of small dissipation on the onset of one-dimensional shock waves. (English. Russian original) Zbl 1010.76505

J. Appl. Math. Mech. 65, No. 3, 441-451 (2001); translation from Prikl. Mat. Mekh. 65, No. 3, 456-466 (2001).
Reviewer: A.E.Babaev (Kyïv)
MSC:  76G25 76L05
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The asymptotic eigenfunctions of the operator \(\nabla D(x,y)\nabla\) corresponding to Liouville metrics and waves on water captured by bottom irregularities. (English. Russian original) Zbl 0926.35103

Math. Notes 64, No. 3, 357-363 (1998); translation from Mat. Zametki 64, No. 3, 414-422 (1998).
MSC:  35P10 35Q35 35L05
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Singularities of the Green function of the nonstationary Schrödinger equation. (English. Russian original) Zbl 0920.35008

Funct. Anal. Appl. 32, No. 2, 132-134 (1998); translation from Funkts. Anal. Prilozh. 32, No. 2, 80-83 (1998).
MSC:  35A20 81Q05
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