Доцент, к.ф.-м.н.

PURE СПбГУ

 Научные интересы

• Асимптотические методы в применении к задачам квантовой механики, оптики, теории волноводов (акустических, упругих, электромагнитных), фотонным кристаллам.
• Разработка методов непрерывного вейвлет-анализа для решения дифференциальных уравнений

Основные публикации

1. Jorstad, S. G. et al (2022). Rapid quasi-periodic oscillations in the relativistic jet of BL Lacertae. Nature, 609(7926), 265-268.
2. Gorodnitskiy, E. A., & V. Perel, M. (2022). The Wavelet-Based Integral Formula for the Solutions of the Wave Equation in an Inhomogeneous Medium: Convergence of Integrals. In Integral Methods in Science and Engineering: Applications in Theoretical and Practical Research (pp. 113-125). Cham: Springer International Publishing.
3. Perel, M. V. (2022, May). Asymptotic analysis of tunneling through the potential barrier in graphene placed in a magnetic field. In 2022 Days on Diffraction (DD) (pp. 1-4). IEEE.
4. Gorodnitskiy, E. A., & Perel, M. V. (2021, May). Rigorous mathematical formulation for quasiphotons. A priori estimates. In 2021 Days on Diffraction (DD) (pp. 69-73). IEEE.
5. Perel, M. V. (2021). Quasiphotons for the Nonstationary 2D Dirac Equation. Journal of Mathematical Sciences, 252, 687-694.
6. Fialkovsky, I., & Perel, M. (2020). Mode transformation for a Schrödinger type equation: Avoided and unavoidable level crossings. Journal of Mathematical Physics, 61(4), 043506.
7. Kuydin, V. V., & Perel, M. V. (2019, June). Gaussian beams for 2D Dirac equation with an electromagnetic field. In 2019 Days on Diffraction (DD) (pp. 111-116). IEEE.
8. Perel, M. V., & Gorodnitskiy, E. A. (2019). Decomposition of Solutions of the Wave Equation into Poincare Wavelets. In Integral Methods in Science and Engineering (pp. 343-352). Birkhauser, Cham.
9. Gorodnitskii, E. A., & Perel’, M. V. (2017). Justification of the wavelet-based integral representation of a solution of the wave equation. Zapiski Nauchnykh Seminarov POMI, 461, 107-123.
10. Gorodnitskiy, E., Perel, M., Geng, Y., & Wu, R. S. (2016). Depth migration with Gaussian wave packets based on Poincare wavelets. Geophys. J. Int., 205(1), 314-331.
11. Fialkovsky, I. V., Perel, M. V., & Plachenov, A. B. (2014). On astigmatic exponentially localized solutions for the wave and the Klein–Gordon–Fock equations. J. Math. Phys., 55(11), 112902.
12. Maria Perel and Evgeny Gorodnitskiy (2012) Integral representations of solutions of the wave equation based on relativistic wavelets J. Phys. A: Math. Theor. 45 385203 ?
13. Sidorenko, M. S., & Perel, M. V. (2012). Analytic approach to the directed diffraction in a one-dimensional photonic crystal slab. Phys. Rev. B, 86(3), 035119.
14. Perel, M. V., & Zaika, D. Y. (2011). Asymptotics of surface plasmons on curved interface. In Proceedings of the International Conference Days on Diffraction 2011 (pp. 149-156). IEEE.
15. Perel, M. V., & Sidorenko, M. S. (2009). Wavelet-based integral representation for solutions of the wave equation. J. Phys. A: Math. Theor., 42(37), 375211.
16. Maria V Perel and Mikhail S Sidorenko (2007) New physical wavelet ‘Gaussian wave packet’ J. Phys. A: Math.Theor., 40(13), 3441.
17. Perel, M. V., Kaplunov, J. D., and Rogerson, G. A. (2005) Asymptotic theory of the internal reflection of modes in the varying elastic wave guide, Wave Motion, 41(2), pp. 95-108.
18. Perel M.V., Fialkovsky I.V.(2003) Exact Exponentially Localized Solutions to the Klein-Gordon Equation J. Math. Sci., 117(2), pp. 3994-4000 (7) Kluwer Academic Publishers (Engl. transl. from Zapiski nauch. sem. POMI, 245, p.187-198, 2001)
19. Perel’, M. V., Fialkovskii, I. V., & Kiselev, A. P. (2000). Resonance interaction of bending and shear modes in a non-uniform Timoshenko beam. Zapiski Nauchnykh Seminarov POMI, 264, 258-284.
20. A.P. Kiselev, M.V. Perel (2000) Highly localized solutions of the wave equation, J. Math. Phys. 41(4), 1934–1955.
21. Perel, M. V., & Stesik, O. L. (1997). Numerical simulation of cycle slipping in diurnal variation of phase of VLF field. Radio Science, 32(1), 199-217.
22. Perel’, M. V. (1990). Overexcitation of modes in an anisotropic earth-ionosphere waveguide on transequatorial paths in the presence of two close degeneracy points. Radiophysics and Quantum Electronics, 33(11), 882-889.
23. BUSLAEV, V., & PEREL, M. (1986). Influence of the velocity profile near the surface on the structure of a deep-sea sound field. SOVIET PHYSICS ACOUSTICS-USSR, 32(3), 181-184.
24. BUSLAEV, V., & PEREL, M. (1984). Aсoustic field structure in deep sea at small depths and long-range. VESTNIK LENINGRADSKOGO UNIVERSITETA SERIYA FIZIKA KHIMIYA, (4), 9-17.

Преподавание

1. Асимптотические методы в теории обыкновенных дифференциальных уравнений (4-ый курс, 1 семестр)
2. Лучевой метод (4-ый курс, 2 семестр)
3. Преддипломный семинар для бакалавров

Руководство научной работой студентов и аспирантов

• М.С. Сидоренко, защита канд.диссертации 13 окт. 2016 г.