Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Proc. Steklov Inst. Math. 322, 105--117 (2023; Zbl 07781666); translation from Tr. Mat. Inst. Steklova 322, 111--123 (2023) Full Text: DOI
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
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Rouleux, M. 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 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Theor. Math. Phys. 214, No. 1, 1--23 (2023; Zbl 1519.35061); translation from Teor. Mat. Fiz. 214, No. 1, 3--29 (2023) Full Text: DOI
Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E. Asymptotic solutions of the Cauchy problem for the nonlinear shallow water equations in a basin with a gently sloping beach. (English) Zbl 1490.76035 Russ. J. Math. Phys. 29, No. 1, 28-36 (2022). MSC: 76B15 35Q35 35B40 76M45 35B27 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 29, No. 1, 28--36 (2022; Zbl 1490.76035) Full Text: DOI
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 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 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., St. Petersbg. Math. J. 33, No. 2, 185--205 (2022; Zbl 1485.35307); translation from Algebra Anal. 33, No. 2, 5--34 (2021) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 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). MSC: 35B27 35L05 35L15 81Q20 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, in: 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. 77--102 (2021; Zbl 1501.35031) Full Text: DOI
Dobrokhotov, Sergey Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I. 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). MSC: 81Q20 35L15 35L45 35S10 53D12 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. Math. Surv. 76, No. 5, 745--819 (2021; Zbl 1492.81056); translation from Usp. Mat. Nauk 76, No. 5, 3--80 (2021) Full Text: DOI
Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E. 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). MSC: 81Q20 81S08 33C10 35B40 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Theor. Math. Phys. 208, No. 2, 1018--1037 (2021; Zbl 1471.81033); translation from Teor. Mat. Fiz. 208, No. 2, 196--217 (2021) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Schafarevich, A. I. Canonical operator on punctured Lagrangian manifolds. (English) Zbl 1462.35480 Russ. J. Math. Phys. 28, No. 1, 22-36 (2021). MSC: 35S05 35Q35 53D12 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 28, No. 1, 22--36 (2021; Zbl 1462.35480) Full Text: DOI
Dobrokhotov, Sergei; Nazaikinskii, Vladimir 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). MSC: 81Q20 35L80 81S10 53D12 53D22 PDFBibTeX XMLCite \textit{S. Dobrokhotov} and \textit{V. Nazaikinskii}, in: Geometric methods in physics XXXVIII. Workshop, Białowieża, Poland, June 30 -- July 6, 2019. Cham: Birkhäuser. 187--195 (2020; Zbl 1472.81099) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Math. Notes 108, No. 3, 318--338 (2020; Zbl 1483.53094); translation from Mat. Zametki 108, No. 3, 334--359 (2020) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 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). MSC: 35G10 35Q35 35Q41 35Q61 81Q20 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Comput. Math. Math. Phys. 60, No. 8, 1348--1360 (2020; Zbl 1450.35119); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 8, 1394--1407 (2020) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Math. Notes 107, No. 5, 847--853 (2020; Zbl 1455.76019); translation from Mat. Zametki 107, No. 5, 780--786 (2020) 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
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 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). MSC: 81Q10 81Q20 33C10 34L40 34E10 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Theor. Math. Phys. 201, No. 3, 1742--1770 (2019; Zbl 1441.81091); translation from Teor. Mat. Fiz. 201, No. 3, 382--414 (2019) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 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). Reviewer: Fatma Hıra (Atakum) MSC: 34L10 34L15 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Proc. Steklov Inst. Math. 306, 74--89 (2019; Zbl 1452.34085); translation from Tr. Mat. Inst. Steklova 306, 83--99 (2019) Full Text: DOI
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 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 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Math. Notes 105, No. 5, 789--794 (2019; Zbl 1426.37049); translation from Mat. Zametki 105, No. 5, 792--797 (2019) Full Text: DOI
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 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 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Differ. Equ. 55, No. 5, 644--657 (2019; Zbl 1418.37094); translation from Differ. Uravn. 55, No. 5, 660--672 (2019) Full Text: DOI
Anikin, Anatoly; Dobrokhotov, Sergey; Nazaikinskii, Vladimir Asymptotic solutions of the wave equation with degenerate velocity and with right-hand side localized in space and time. (English) Zbl 1428.35191 J. Math. Phys. Anal. Geom. 14, No. 4, 393-405 (2018). MSC: 35L15 35L05 PDFBibTeX XMLCite \textit{A. Anikin} et al., J. Math. Phys. Anal. Geom. 14, No. 4, 393--405 (2018; Zbl 1428.35191) Full Text: DOI Link
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 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 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Math. Notes 104, No. 4, 471--488 (2018; Zbl 1420.35151); translation from Mat. Zametki 104, No. 4, 483--504 (2018) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Efficient formulas for the Maslov canonical operator near a simple caustic. (English) Zbl 1406.81036 Russ. J. Math. Phys. 25, No. 4, 545-552 (2018). MSC: 81Q20 53D12 34L40 70H15 81-08 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Russ. J. Math. Phys. 25, No. 4, 545--552 (2018; Zbl 1406.81036) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, Anna V. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Math. Notes 103, No. 5, 713--723 (2018; Zbl 1397.42004); translation from Mat. Zametki 103, No. 5, 680--692 (2018) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Waves on the free surface described by linearized equations of hydrodynamics with localized right-hand sides. (English) Zbl 1388.76028 Russ. J. Math. Phys. 25, No. 1, 1-16 (2018). MSC: 76B07 76B15 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Russ. J. Math. Phys. 25, No. 1, 1--16 (2018; Zbl 1388.76028) Full Text: DOI
Anikin, Anatoly; Dobrokhotov, Sergey; Nazaikinskii, Vladimir; Rouleux, Michel Semi-classical Green functions. arXiv:1808.00047 Preprint, arXiv:1808.00047 [math-ph] (2018). BibTeX Cite \textit{A. Anikin} et al., ``Semi-classical Green functions'', Preprint, arXiv:1808.00047 [math-ph] (2018) Full Text: arXiv OA License
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. On the asymptotics of a Bessel-type integral having applications in wave run-up theory. (English. Russian original) Zbl 1384.42001 Math. Notes 102, No. 6, 756-762 (2017); translation from Mat. Zametki 102, No. 6, 828-835 (2017). MSC: 42A38 35L05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Math. Notes 102, No. 6, 756--762 (2017; Zbl 1384.42001); translation from Mat. Zametki 102, No. 6, 828--835 (2017) 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
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Rouleux, M. 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 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Dokl. Math. 96, No. 1, 406--410 (2017; Zbl 1377.35062); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 475, No. 6, 624--628 (2016) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Math. Notes 101, No. 6, 1053--1060 (2017; Zbl 1516.35040); translation from Mat. Zametki 101, No. 6, 936--942 (2017) 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
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Propagation of a linear wave created by a spatially localized perturbation in a regular lattice and punctured Lagrangian manifolds. (English) Zbl 1376.37114 Russ. J. Math. Phys. 24, No. 1, 127-133 (2017). MSC: 37K60 53D12 35S10 39A12 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Russ. J. Math. Phys. 24, No. 1, 127--133 (2017; Zbl 1376.37114) Full Text: DOI
Dobrokhotov, Sergei Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I. 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). MSC: 81Q20 53D12 35C20 35S30 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Izv. Math. 81, No. 2, 286--328 (2017; Zbl 1369.81033); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 81, No. 2, 53--96 (2017) Full Text: DOI
Maslov, V. P.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Volume and entropy in abstract analytic number theory and thermodynamics. (English. Russian original) Zbl 1362.82025 Math. Notes 100, No. 6, 828-834 (2016); translation from Mat. Zametki 100, No. 6, 855-867 (2016). MSC: 82B30 82D05 11N80 PDFBibTeX XMLCite \textit{V. P. Maslov} et al., Math. Notes 100, No. 6, 828--834 (2016; Zbl 1362.82025); translation from Mat. Zametki 100, No. 6, 855--867 (2016) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Math. Notes 100, No. 5, 695--713 (2016; Zbl 1362.35170); translation from Mat. Zametki 100, No. 5, 710--731 (2016) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Shafarevich, A. I. 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). Reviewer: Sönke Hansen (Paderborn) MSC: 53D12 81Q20 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Dokl. Math. 93, No. 1, 99--102 (2016; Zbl 1345.53083); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 466, No. 6, 641--644 (2016) Full Text: DOI
Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E.; Tirozzi, B. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., in: Theory and applications in mathematical physics. Conference in honor of B. Tirozzi's 70th birthday. Hackensack, NJ: World Scientific. 29--47 (2016; Zbl 1329.35246) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Dokl. Math. 91, No. 2, 227--231 (2015; Zbl 1326.35022); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 461, No. 5, 516--520 (2015) Full Text: DOI
Dobrokhotov, S. Yu.; Makrakis, G.; Nazaikinskii, V. E. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Transl., Ser. 2, Am. Math. Soc. 233, 95--115 (2014; Zbl 1320.81058) Full Text: arXiv
Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Theor. Math. Phys. 180, No. 2, 894--916 (2014; Zbl 1323.81031); translation from Teor. Mat. Fiz. 180, No. 2, 162--188 (2014) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data. (English) Zbl 1320.35180 Russ. J. Math. Phys. 20, No. 4, 389-401 (2013). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 35L15 35L05 76B15 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 20, No. 4, 389--401 (2013; Zbl 1320.35180) Full Text: DOI
Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E.; Tudorovskii, T. Ya. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Theor. Math. Phys. 177, No. 3, 1579--1605 (2013; Zbl 1298.81091); translation from Teor. Mat. Fiz. 177, No. 3, 355--386 (2013) Full Text: DOI arXiv
Dobrokhotov, S. Yu.; Lozhnikov, D. A.; Nazaikinskii, V. E. Wave trains associated with a cascade of bifurcations of space-time caustics over elongated underwater banks. (English) Zbl 1338.35390 Math. Model. Nat. Phenom. 8, No. 5, 1-12 (2013). MSC: 35Q53 76B15 35A18 35B40 37G10 74J05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Math. Model. Nat. Phenom. 8, No. 5, 1--12 (2013; Zbl 1338.35390) Full Text: DOI
Dobrokhotov, Sergey; Minenkov, Dmitrii; Nazaikinskii, Vladimir; Tirozzi, Brunello 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). MSC: 35L15 35L05 81Q20 35Q35 PDFBibTeX XMLCite \textit{S. Dobrokhotov} et al., Oper. Theory: Adv. Appl. 228, 95--125 (2013; Zbl 1263.35154) Full Text: DOI arXiv
Dobrokhotov, S. Yu.; Nazaĭkinskiĭ, V. E.; Tirozzi, B. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., St. Petersbg. Math. J. 22, No. 6, 895--911 (2011; Zbl 1230.35057); translation from Algebra Anal. 22, No. 6, 67--90 (2010) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I. (English) Zbl 1387.35404 Russ. J. Math. Phys. 17, No. 4, 434-447 (2010). MSC: 35L60 35C20 35Q35 76B15 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 17, No. 4, 434--447 (2010; Zbl 1387.35404) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. Asymptotic solutions of 2D wave equations with variable velocity and localized right-hand side. (English) Zbl 1192.35110 Russ. J. Math. Phys. 17, No. 1, 66-76 (2010). MSC: 35L15 35B40 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 17, No. 1, 66--76 (2010; Zbl 1192.35110) Full Text: DOI