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Found 29 Documents (Results 1–29)

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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On expansions in the exact and asymptotic eigenfunctions of the one-dimensional Schrödinger operator. (English. Russian original) Zbl 1517.81051

Math. Notes 112, No. 5, 623-641 (2022); translation from Mat. Zametki 112, No. 5, 644-664 (2022).
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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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Airy functions and transition between semiclassical and harmonic oscillator approximations for one-dimensional bound states. (English. Russian original) Zbl 1453.81024

Theor. Math. Phys. 204, No. 2, 984-992 (2020); translation from Teor. Mat. Fiz. 204, No. 2, 171-180 (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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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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Exact step-like solutions of one-dimensional shallow-water equations over a sloping bottom. (English. Russian original) Zbl 1415.35226

Math. Notes 104, No. 6, 915-921 (2018); translation from Mat. Zametki 104, No. 6, 930-936 (2018).
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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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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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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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Random perturbations of invariant Lagrangian tori of Hamiltonian vector fields. (English. Russian original) Zbl 0952.37013

Math. Notes 64, No. 5, 674-679 (1998); translation from Mat. Zametki 64, No. 5, 783-787 (1998).
MSC:  37J25 60H10 58J37
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Asymptotics of linear water waves over a gradually developing bottom. (English) Zbl 0818.35092

Kleinman, Ralph (ed.) et al., Mathematical and numerical aspects of wave propagation. Proceedings of the 2nd international conference held in Newark, DE, USA, June 7-10, 1993. Philadelphia, PA: SIAM. 465-472 (1993).
MSC:  35Q35 76B15 35B40
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Splitting of the lowest energy levels of the Schrödinger equation and asymptotic behavior of the fundamental solution of the equation \(hu_ t=h^ 2\Delta u/2-V(x)u\). (English. Russian original) Zbl 0745.35033

Theor. Math. Phys. 87, No. 3, 561-599 (1991); translation from Teor. Mat. Fiz. 87, No. 3, 323-375 (1991).
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