English

The Malyuzhinets-Popov diffraction problem revisited

Mathematical Physics 2022-12-20 v2 math.MP

Abstract

In this paper, the high-frequency diffraction of a plane wave incident along a planar boundary turning into a smooth convex contour, so that the curvature undergoes a jump, is asymptotically analysed. An approach modifying the Fock parabolic-equation method is developed. Asymptotic formulas for the wavefield in the illuminated area, shadow, and the penumbra are derived. The penumbral field is characterized by novel and previously unseen special functions that resemble Fock's integrals.

Keywords

Cite

@article{arxiv.2206.05444,
  title  = {The Malyuzhinets-Popov diffraction problem revisited},
  author = {Ekaterina A. Zlobina and Aleksei P. Kiselev},
  journal= {arXiv preprint arXiv:2206.05444},
  year   = {2022}
}

Comments

30 pages, 4 figures. Submitted to Wave Motion 03.03.2022. Resubmitted to Wave Motion 29.11.2022

R2 v1 2026-06-24T11:47:22.034Z