Maria V. Perel

1

Associate professor

PURE SPBU

 Directions of research

  • Asymptotic methods for problems of quantum mechanics, optics, the theory of waveguides (acoustic, elastic, electromagnetic), photonic crystals.
  • Continuous wavelet analysis methods for solutions of differential equations

Basic Research papers

  1. М.В. Перель (2019), Квазифотоны для нестационарного 2D уравнения Дирака. Зап. науч. сем. ПОМИ, 483, 178-188.
  2. V.V. Kuydin, M.V. Perel (2019) Gaussian beams for 2D Dirac equation with electromagnetic field. In Proceedings of the International Conference Days on Diffraction 2019, (pp. 111-116), IEEE.
  3. Ignat Fialkovsky, Maria Perel (2019) Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings, arXiv:1901.01984, submitted.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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 ?
  9. 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.
  10. 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.
  11. 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.
  12. Maria V Perel and Mikhail S Sidorenko (2007) New physical wavelet ‘Gaussian wave packet’ J. Phys. A: Math.Theor., 40(13), 3441.
  13. 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.
  14. 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)
  15. 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.
  16. A.P. Kiselev, M.V. Perel (2000) Highly localized solutions of the wave equation, J. Math. Phys. 41(4), 1934–1955.
  17. 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.
  18. 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.
  19. 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.
  20. 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.

Teaching

  1. Asymptotic methods in the theory of ordinary differential equations (for students of the 4th year, Autumn semester)
  2. Ray method (for students of the 4th year, Spring semester)
  3. Scientific seminar for bachelors

Scientific supervisor of undergraduate, graduate and post-graduate students

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