Maria V. Perel

DSC_9704

Associate professor

PURE SPBU

 Directions of research

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

Basic Research papers

  1. Fialkovsky I. V., Perel M. V., Plachenov A. B. On astigmatic exponentially localized solutions for the wave and the Klein–Gordon–Fock equations //Journal of Mathematical Physics. – 2014. – Т. 55. – №. 11. – С. 112902.
  2. Perel M., Gorodnitskiy E. Integral representations of solutions of the wave equation based on relativistic wavelets //Journal of Physics A: Mathematical and Theoretical. – 2012. – Т. 45. – №. 38. – С. 385203.
  3. Sidorenko M. S., Perel M. V. Analytic approach to the directed diffraction in a one-dimensional photonic crystal slab //Physical Review B. –
    2012. – Т. 86. – №. 3. – С. 035119.
  4. Perel M. V., Sidorenko M. S. Wavelet-based integral representation for solutions of the wave equation //Journal of Physics A: Mathematical and Theoretical. – 2009. – Т. 42. – №. 37. – С. 375211.
  5. Perel M. V., Sidorenko M. S. New physical wavelet’Gaussian wave packet’ //Journal of Physics A: Mathematical and Theoretical. – 2007. – Т. 40.
    – №. 13. – С. 3441.
  6. Perel M. V., Kaplunov J. D., Rogerson G. A. An asymptotic theory for internal reflection in weakly inhomogeneous elastic waveguides //Wave motion. –
    2005. – Т. 41. – №. 2. – С. 95-108.
  7. Gorodnitskiy, E., Perel, M., Geng, Y. and Wu, R.S., 2016. Depth migration with Gaussian wave packets based on Poincaré wavelets. Geophysical Journal International, 205(1), pp.314-331.

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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