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
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Shkalikov, A. A. 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). MSC: 81Q10 34L40 34L20 81Q20 34L15 33C10 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Math. Notes 112, No. 5, 623--641 (2022; Zbl 1517.81051); translation from Mat. Zametki 112, No. 5, 644--664 (2022) 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, 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
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Tsvetkova, A. V. 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). MSC: 81Q10 81Q20 35P05 35B40 33C10 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Theor. Math. Phys. 204, No. 2, 984--992 (2020; Zbl 1453.81024); translation from Teor. Mat. Fiz. 204, No. 2, 171--180 (2020) 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
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, Sergei Yu.; Minenkov, Dmitrii S.; Neishtadt, Anatoly I.; Shlosman, Semen B. Classical and quantum dynamics of a particle in a narrow angle. (English) Zbl 1434.35135 Regul. Chaotic Dyn. 24, No. 6, 704-716 (2019). MSC: 35Q40 35J10 35P20 35B40 33C10 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Regul. Chaotic Dyn. 24, No. 6, 704--716 (2019; Zbl 1434.35135) Full Text: DOI
Aksenov, A. V.; Dobrokhotov, S. Yu.; Druzhkov, K. P. 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). Reviewer: Guanggan Chen (Chengdu) MSC: 35Q35 76B15 35B40 35B20 PDFBibTeX XMLCite \textit{A. V. Aksenov} et al., Math. Notes 104, No. 6, 915--921 (2018; Zbl 1415.35226); translation from Mat. Zametki 104, No. 6, 930--936 (2018) Full Text: DOI
Dobrokhotov, S. Yu.; Tsvetkova, A. V. Lagrangian manifolds related to the asymptotics of Hermite polynomials. (English. Russian original) Zbl 1409.42019 Math. Notes 104, No. 6, 810-822 (2018); translation from Mat. Zametki 104, No. 6, 835-850 (2018). MSC: 42C05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{A. V. Tsvetkova}, Math. Notes 104, No. 6, 810--822 (2018; Zbl 1409.42019); translation from Mat. Zametki 104, No. 6, 835--850 (2018) Full Text: DOI
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.; 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. 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
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. 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.; 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, S. Yu.; Minenkov, D. S. On various averaging methods for a nonlinear oscillator with slow time-dependent potential and a nonconservative perturbation. (English) Zbl 1209.34050 Regul. Chaotic Dyn. 15, No. 2-3, 285-299 (2010). MSC: 34C29 34C15 34E05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{D. S. Minenkov}, Regul. Chaotic Dyn. 15, No. 2--3, 285--299 (2010; Zbl 1209.34050) Full Text: DOI
Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B. Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations. (English) Zbl 1180.35336 Russ. J. Math. Phys. 15, No. 2, 192-221 (2008). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 35L45 35B05 35B40 35Q35 37J05 47G30 76B15 76B47 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 15, No. 2, 192--221 (2008; Zbl 1180.35336) Full Text: DOI
Boutet de Monvel, A.; Dobrokhotov, S. Yu. 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). Reviewer: Yu.Kifer (Jerusalem) MSC: 37J25 60H10 58J37 PDFBibTeX XMLCite \textit{A. Boutet de Monvel} and \textit{S. Yu. Dobrokhotov}, Math. Notes 64, No. 5, 674--679 (1998; Zbl 0952.37013); translation from Mat. Zametki 64, No. 5, 783--787 (1998) Full Text: DOI
Dobrokhotov, Sergei Yu.; Kolokol’tsov, Vassili N. The double-well splitting of the low energy levels for the Schrödinger operator of discrete \(\varphi^ 4\)-models on tori. (English) Zbl 0820.60097 J. Math. Phys. 36, No. 3, 1038-1053 (1995). MSC: 60K40 82B44 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. N. Kolokol'tsov}, J. Math. Phys. 36, No. 3, 1038--1053 (1995; Zbl 0820.60097) Full Text: DOI
Zhevandrov, P. N.; Dobrokhotov, S. Yu.; Kuzmina, V. M. 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 PDFBibTeX XMLCite \textit{P. N. Zhevandrov} et al., in: 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; Zbl 0818.35092)
Dobrokhotov, S. Yu.; Kolokoltsov, V. N.; Maslov, V. P. Quantization of the Bellman equation, exponential asymptotics and tunneling. (English) Zbl 0796.35141 Maslov, V. P. (ed.) et al., Idempotent analysis. Transl. ed. by A.B. Sossinskij. Providence, RI: American Mathematical Society. Adv. Sov. Math. 13, 1-46 (1992). MSC: 35Q40 35B40 35F20 90C27 81Q20 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Adv. Sov. Math. 13, 1--46 (1992; Zbl 0796.35141)
Dobrokhotov, S. Yu.; Kolokol’tsov, V. N.; Maslov, V. P. 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). MSC: 35J10 35P20 81Q20 35B40 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Theor. Math. Phys. 87, No. 3, 561--599 (1991; Zbl 0745.35033); translation from Teor. Mat. Fiz. 87, No. 3, 323--375 (1991) Full Text: DOI
Dobrokhotov, S. Yu.; Maslov, V. P. Asymptotics of a spectral boundary-value problem for a nonlinear equation for semiconductors. (English. Russian original) Zbl 0423.35070 Sov. Phys., Dokl. 23, 894-896 (1978); translation from Dokl. Akad. Nauk SSSR 243, 897-900 (1978). MSC: 35P15 35Q99 35C20 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. P. Maslov}, Sov. Phys., Dokl. 23, 894--896 (1978; Zbl 0423.35070); translation from Dokl. Akad. Nauk SSSR 243, 897--900 (1978)