
doi: 10.1007/bf01119359
In this work the wave field arising over a concave-convex reflecting boundary is studied in the Kirchhoff approximation. The field arises as a result of the incidence of whispering gallery waves on an inflection point of the boundary from the concave side. The shortwave asymptotics of the Kirchhoff integral are obtained which is expressed in terms of special functions in a neighborhood of the inflection point of the boundary and in a neighborhood of the tangent to the boundary at the inflection point. Diagrams are constructed that illustrate the behavior of the scattered field.
Schrödinger operator, Schrödinger equation, whispering gallery wave, radiation field, wave field over a reflex surface, Kirchhoff approximation, Waves and radiation in optics and electromagnetic theory, flex point, short wave asymptotics, Asymptotic expansions of solutions to PDEs
Schrödinger operator, Schrödinger equation, whispering gallery wave, radiation field, wave field over a reflex surface, Kirchhoff approximation, Waves and radiation in optics and electromagnetic theory, flex point, short wave asymptotics, Asymptotic expansions of solutions to PDEs
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 3 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
