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Vybornyi, E. V.; Rumyantseva, S. V.

Semiclassical asymptotics of oscillating tunneling for a quadratic Hamiltonian on the algebra \(\operatorname{su}(1,1)\). (English. Russian original) Zbl 1517.81056

Math. Notes 112, No. 5, 642-655 (2022); translation from Mat. Zametki 112, No. 5, 665-681 (2022).
MSC:  81Q20 81U26 37D30 17B45 81R30 32A19 14D21 35P15
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\textit{E. V. Vybornyi} and \textit{S. V. Rumyantseva}, Math. Notes 112, No. 5, 642--655 (2022; Zbl 1517.81056); translation from Mat. Zametki 112, No. 5, 665--681 (2022)
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Eliseev, A. G.

The regularized asymptotics of a solution of the Cauchy problem in the presence of a weak turning point of the limit operator. (English. Russian original) Zbl 1493.34164

Sb. Math. 212, No. 10, 1415-1435 (2021); translation from Mat. Sb. 212, No. 10, 76-95 (2021).
Reviewer: Robert Vrabel (Trnava)
MSC:  34E20 34A12 34E05
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\textit{A. G. Eliseev}, Sb. Math. 212, No. 10, 1415--1435 (2021; Zbl 1493.34164); translation from Mat. Sb. 212, No. 10, 76--95 (2021)
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Mikhasev, G. I.

A study of free high-frequency vibrations of an inhomogeneous nanorod, based on the nonlocal theory of elasticity. (English. Russian original) Zbl 1471.74024

Vestn. St. Petersbg. Univ., Math. 54, No. 2, 125-134 (2021); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 8(66), No. 2, 220-232 (2021).
MSC:  74H45 74K10 74M25 74H10 74B99
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\textit{G. I. Mikhasev}, Vestn. St. Petersbg. Univ., Math. 54, No. 2, 125--134 (2021; Zbl 1471.74024); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 8(66), No. 2, 220--232 (2021)
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Eremin, Yu. A.; Sveshnikov, A. G.

Semi-classical models of quantum nanoplasmonics based on the discrete source method (review). (English. Russian original) Zbl 1466.78010

Comput. Math. Math. Phys. 61, No. 4, 564-590 (2021); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 4, 580-607 (2021).
MSC:  78A40 78A48 78A35 81Q20
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\textit{Yu. A. Eremin} and \textit{A. G. Sveshnikov}, Comput. Math. Math. Phys. 61, No. 4, 564--590 (2021; Zbl 1466.78010); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 4, 580--607 (2021)
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Crouseilles, Nicolas; Jin, Shi; Lemou, Mohammed; Liu, Liu

Nonlinear geometric optics based multiscale stochastic Galerkin methods for highly oscillatory transport equations with random inputs. (English) Zbl 1471.65137

ESAIM, Math. Model. Numer. Anal. 54, No. 6, 1849-1882 (2020).
Reviewer: Alain Brillard (Riedisheim)
MSC:  65M60 35L03 35Q40 35Q49 60H35 65D32 65L06 65M12 65M75 65M70 81Q20
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\textit{N. Crouseilles} et al., ESAIM, Math. Model. Numer. Anal. 54, No. 6, 1849--1882 (2020; Zbl 1471.65137)
Full Text: DOI arXiv
Tsvetkova, A. V.; Shafarevich, A. I.

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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\textit{A. V. Tsvetkova} and \textit{A. I. Shafarevich}, Math. Notes 108, No. 4, 590--602 (2020; Zbl 1451.35243); translation from Mat. Zametki 108, No. 4, 601--616 (2020)
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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
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\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)
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Eliseev, Aleksandr Georgievich; Kirichenko, Pavel Vladimirovich

Regularized asymptotics of solution a singularly perturbed Cauchy problem in the presence of the “weak” turning point at the limit operator. (Russian. English summary) Zbl 1450.34040

Differ. Uravn. Protsessy Upr. 2020, No. 1, 55-67 (2020).
Reviewer: Robert Vrabel (Trnava)
MSC:  34E15 34A30 34A12 34E05 34E20
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\textit{A. G. Eliseev} and \textit{P. V. Kirichenko}, Differ. Uravn. Protsessy Upr. 2020, No. 1, 55--67 (2020; Zbl 1450.34040)
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Migaeva, A. S.; Pereskokov, A. V.

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).
MSC:  47Nxx 33Cxx 81Vxx 81Rxx
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\textit{A. S. Migaeva} and \textit{A. V. Pereskokov}, Math. Notes 107, No. 5, 804--819 (2020; Zbl 07215589); translation from Mat. Zametki 107, No. 5, 734--751 (2020)
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del Valle, J. C.; Turbiner, A. V.

Radial anharmonic oscillator: perturbation theory, new semiclassical expansion, approximating eigenfunctions. I: Generalities, cubic anharmonicity case. (English) Zbl 1471.81019

Int. J. Mod. Phys. A 34, No. 26, Article ID 1950143, 43 p. (2019).
MSC:  81Q05 81Q15 81Q20 35A15 81S40 70J35 41A58 35P15
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\textit{J. C. del Valle} and \textit{A. V. Turbiner}, Int. J. Mod. Phys. A 34, No. 26, Article ID 1950143, 43 p. (2019; Zbl 1471.81019)
Full Text: DOI arXiv
Novokshenov, V. Yu.

Movable poles of Painlevé I transcendents and singularities of monodromy data manifolds. (English) Zbl 1427.34118

Buchstaber, Victor M. (ed.) et al., Recent developments in integrable systems and related topics of mathematical physics. Kezenoi-Am, Russia, 2016. Cham: Springer. Springer Proc. Math. Stat. 273, 24-37 (2018).
Reviewer: Dmitry Artamonov (Moskva)
MSC:  34M55 34M35 34M05 34M60 34M56
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\textit{V. Yu. Novokshenov}, Springer Proc. Math. Stat. 273, 24--37 (2018; Zbl 1427.34118)
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Fedotov, A.; Shchetka, E.

Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial. (English. Russian original) Zbl 1385.39001

St. Petersbg. Math. J. 29, No. 2, 363-381 (2018); translation from Algebra Anal. 29, No. 2, 193-219 (2017).
MSC:  39A12 34E20 34L40 39A22
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\textit{A. Fedotov} and \textit{E. Shchetka}, St. Petersbg. Math. J. 29, No. 2, 363--381 (2018; Zbl 1385.39001); translation from Algebra Anal. 29, No. 2, 193--219 (2017)
Full Text: DOI
Fedotov, A. A.; Shchetka, E. V.

The complex WKB method for difference equations in bounded domains. (English. Russian original) Zbl 1476.39025

J. Math. Sci., New York 224, No. 1, 157-169 (2017); translation from Zap. Nauchn. Semin. POMI 438, 236-256 (2015).
MSC:  39A70 34E20 39A12 39B32
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\textit{A. A. Fedotov} and \textit{E. V. Shchetka}, J. Math. Sci., New York 224, No. 1, 157--169 (2017; Zbl 1476.39025); translation from Zap. Nauchn. Semin. POMI 438, 236--256 (2015)
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Bukzhalev, E. E.

The Cauchy problem for singularly perturbed weakly nonlinear second-order differential equations: an iterative method. (English. Russian original) Zbl 1394.65049

Mosc. Univ. Comput. Math. Cybern. 41, No. 3, 113-121 (2017); translation from Vestn. Mosk. Univ., Ser. XV 2017, No. 3, 10-17 (2017).
Reviewer: Srinivasan Natesan (Assam)
MSC:  65L05 34E05 34E20 34E15 34A45 34B05
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\textit{E. E. Bukzhalev}, Mosc. Univ. Comput. Math. Cybern. 41, No. 3, 113--121 (2017; Zbl 1394.65049); translation from Vestn. Mosk. Univ., Ser. XV 2017, No. 3, 10--17 (2017)
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Dunne, Gerald V.; Ünsal, Mithat

WKB and resurgence in the Mathieu equation. (English) Zbl 1414.81105

Fauvet, Frédéric (ed.) et al., Resurgence, physics and numbers, Pisa, Italy, May 18–22, 2015. Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series 20. Pisa: Edizioni della Normale; Pisa: Scuola Normale Superiore. 249-298 (2017).
Reviewer: Nicolae Lupa (Timisoara)
MSC:  81Q10 81Q20 34B30
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\textit{G. V. Dunne} and \textit{M. Ünsal}, CRM Ser. 20, 249--298 (2017; Zbl 1414.81105)
Full Text: DOI arXiv
Melezhik, Vladimir S.; Sevastianov, Leonid A.

Quantum-semiclassical calculation of transition probabilities in antiproton collisions with helium ions. (English) Zbl 1385.81046

Rykov, Vladimir V. (ed.) et al., Analytical and computational methods in probability theory. First international conference, ACMPT 2017, Moscow, Russia, October 23–27, 2017. Proceedings. Cham: Springer (ISBN 978-3-319-71503-2/pbk; 978-3-319-71504-9/ebook). Lecture Notes in Computer Science 10684, 449-460 (2017).
MSC:  81U35 81V35 81Q05 81Q20 39A12 81V45
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\textit{V. S. Melezhik} and \textit{L. A. Sevastianov}, Lect. Notes Comput. Sci. 10684, 449--460 (2017; Zbl 1385.81046)
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Hnatich, M.; Khmara, Viktor M.; Lazur, Volodymyr Yu.; Reity, Oleksandr K.

The WKB method for the quantum mechanical two-Coulomb-center problem. (English. Russian original) Zbl 1369.81034

Theor. Math. Phys. 190, No. 3, 345-358 (2017); translation from Teor. Mat. Fiz. 190, No. 3, 403-418 (2017).
MSC:  81Q20 81V35
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\textit{M. Hnatich} et al., Theor. Math. Phys. 190, No. 3, 345--358 (2017; Zbl 1369.81034); translation from Teor. Mat. Fiz. 190, No. 3, 403--418 (2017)
Full Text: DOI
Mortell, Michael P.; Seymour, Brian R.

Nonlinear waves in bounded media. The mathematics of resonance. (English) Zbl 1373.76002

Hackensack, NJ: World Scientific (ISBN 978-981-3100-33-6/hbk; 978-981-3100-35-0). xiv, 405 p. (2017).
Reviewer: Fiazud Din Zaman (Dhahran)
MSC:  76-02 74-02 76B15 76B70 74J30 76Q05 00A79
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\textit{M. P. Mortell} and \textit{B. R. Seymour}, Nonlinear waves in bounded media. The mathematics of resonance. Hackensack, NJ: World Scientific (2017; Zbl 1373.76002)
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