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Found 45 Documents (Results 1–45)

Nonlinear effects and run-up of coastal waves generated by billiards with semi-rigid walls in the framework of shallow water theory. (English. Russian original) Zbl 07781666

Proc. Steklov Inst. Math. 322, 105-117 (2023); translation from Tr. Mat. Inst. Steklova 322, 111-123 (2023).
MSC:  76B15 76M45 86A05
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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
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Lagrangian manifolds and the construction of asymptotics for (pseudo)differential equations with localized right-hand sides. (English. Russian original) Zbl 1519.35061

Theor. Math. Phys. 214, No. 1, 1-23 (2023); translation from Teor. Mat. Fiz. 214, No. 1, 3-29 (2023).
MSC:  35C20 35S05 53D12
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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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Homogenization of the Cauchy problem for the wave equation with rapidly varying coefficients and initial conditions. (English) Zbl 1501.35031

Manuilov, Vladimir M. (ed.) et al., Differential equations on manifolds and mathematical physics. Dedicated to the memory of Boris Sternin. Selected papers based on the presentations of the conference on partial differential equations and applications, Moscow, Russia, November 6–9, 2018. Cham: Birkhäuser. Trends Math., 77-102 (2021).
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Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations. (English. Russian original) Zbl 1492.81056

Russ. Math. Surv. 76, No. 5, 745-819 (2021); translation from Usp. Mat. Nauk 76, No. 5, 3-80 (2021).
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Representation of Bessel functions by the Maslov canonical operator. (English. Russian original) Zbl 1471.81033

Theor. Math. Phys. 208, No. 2, 1018-1037 (2021); translation from Teor. Mat. Fiz. 208, No. 2, 196-217 (2021).
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Fock quantization of canonical transformations and semiclassical asymptotics for degenerate problems. (English) Zbl 1472.81099

Kielanowski, Piotr (ed.) et al., Geometric methods in physics XXXVIII. Workshop, Białowieża, Poland, June 30 – July 6, 2019. Cham: Birkhäuser. Trends Math., 187-195 (2020).
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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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Efficient asymptotics in problems on the propagation of waves generated by localized sources in linear multidimensional inhomogeneous and dispersive media. (English. Russian original) Zbl 1450.35119

Comput. Math. Math. Phys. 60, No. 8, 1348-1360 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 8, 1394-1407 (2020).
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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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Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems. (English. Russian original) Zbl 1441.81091

Theor. Math. Phys. 201, No. 3, 1742-1770 (2019); translation from Teor. Mat. Fiz. 201, No. 3, 382-414 (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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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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The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides. (English. Russian original) Zbl 1377.35062

Dokl. Math. 96, No. 1, 406-410 (2017); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 475, No. 6, 624-628 (2016).
MSC:  35J05
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Punctured Lagrangian manifolds and asymptotic solutions of the linear water wave equations with localized initial conditions. (English. Russian original) Zbl 1516.35040

Math. Notes 101, No. 6, 1053-1060 (2017); translation from Mat. Zametki 101, No. 6, 936-942 (2017).
MSC:  35B25 35C20 35Q35
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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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New integral representations of the Maslov canonical operator in singular charts. (English. Russian original) Zbl 1369.81033

Izv. Math. 81, No. 2, 286-328 (2017); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 81, No. 2, 53-96 (2017).
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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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Maslov’s canonical operator in arbitrary coordinates on the Lagrangian manifold. (English. Russian original) Zbl 1345.53083

Dokl. Math. 93, No. 1, 99-102 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 466, No. 6, 641-644 (2016).
MSC:  53D12 81Q20
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Simple exact and asymptotic solutions of the 1D run-up problem over a slowly varying (quasiplanar) bottom. (English) Zbl 1329.35246

Agliari, Elena (ed.) et al., Theory and applications in mathematical physics. Conference in honor of B. Tirozzi’s 70th birthday. Hackensack, NJ: World Scientific (ISBN 978-981-4713-27-6/hbk; 978-981-4713-29-0/ebook). 29-47 (2016).
MSC:  35Q35 76B15 76M45
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On a homogenization method for differential operators with oscillating coefficients. (English. Russian original) Zbl 1326.35022

Dokl. Math. 91, No. 2, 227-231 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 461, No. 5, 516-520 (2015).
MSC:  35B27 35L15
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Fourier integrals and a new representation of Maslov’s canonical operator near caustics. (English) Zbl 1320.81058

Khruslov, E. (ed.) et al., Spectral theory and differential equations: V. A. Marchenko’s 90th anniversary collection. Providence, RI: American Mathematical Society (AMS); (ISBN 978-1-4704-1683-6/hbk). Translations. Series 2. American Mathematical Society 233; Advances in the Mathematical Sciences 66, 95-115 (2014).
MSC:  81Q20 35S30 53D12
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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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New formulas for Maslov’s canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics. (English. Russian original) Zbl 1298.81091

Theor. Math. Phys. 177, No. 3, 1579-1605 (2013); translation from Teor. Mat. Fiz. 177, No. 3, 355-386 (2013).
MSC:  81Q20 81Q05
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Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. (English) Zbl 1263.35154

Karlovich, Yuri I. (ed.) et al., Operator theory, pseudo-differential equations, and mathematical physics. The Vladimir Rabinovich anniversary volume. Dedicated to his 70th birthday. Basel: Birkhäuser (ISBN 978-3-0348-0536-0/hbk; 978-3-0348-0537-7/ebook). Operator Theory: Advances and Applications 228, 95-125 (2013).
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Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data. (English. Russian original) Zbl 1230.35057

St. Petersbg. Math. J. 22, No. 6, 895-911 (2011); translation from Algebra Anal. 22, No. 6, 67-90 (2010).
MSC:  35L15 35C20 78A05
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