have wideband and ultra wideband properties, and also an extensive range of practical
applications from scanning of space depths to domestic application [6-8]. Model
problems of wave diffraction by such surfaces were considered in works [7-15] where
authors used both approximate methods [7] and rigorous methods for boundary value
problems solution [8-15]. Results of a research of model electromagnetic problems for
conical structures, conical and plane angular sectors, and also their combinations, can
be effectively used in designing, development and creation of modern radar complexes,
devices for diagnostics and control [16-18].
In the monograph [7] results of the research of a problem of plane electromagnetic
wave diffraction by a solid perfectly conductive cone in the assumption that its linear
size considerably exceeds the length of the incident wave were given. In approximation
of physical optics and physical theory of diffraction the representations for fields and
scattering cross section were obtained, that allowed to determine the radar cross section
of the solid cone. Contributions of the edge wave and the wave scattered from the tip
were marked out in the representation of scattered field.
In classical works [8, 9] rigorous analytical solutions of boundary value problems
of wave diffraction by solid circular and elliptical semi-infinite perfectly conductive
cones are given by reducing such problems to the boundary value problems of
mathematical physics. The idea of using in these works the variable separation method
for the solution of the first and second boundary value problems of the Helmholtz
equation, representation of solution in the form of eigenfunction series and application
of integral transforms were fundamental for subsequent researches of boundary
electromagnetic value problems with conical geometry by other authors [10-15].
In [10] the research of the problem of scalar plane harmonic wave diffraction by
flat, and circular cones with perfectly boundary conditions were performed. On the
basis of using the integral representation and the Green function representation for the
problem on the sphere with a slot in the form of diffraction series it was shown that
various terms of this series correspond to different contributions to wave field of the
conical problem. The diffraction field structure was studied and a uniform asymptotic
contribution for a spherical wave, a geometrically reflected wave, cylindrical waves of
multiple scattering, creeping waves were found.
The article [11] is devoted to the research of a problem of plane acoustic wave
diffraction by a solid transparent semi-infinite cone. Using the incomplete variables
separation method the diffraction problem was reduced to the solution of a singular
integral Fredholm equation. On the basis of the obtained representations for diffraction
coefficients the analysis of the field reflected from a cone and the field passed through
a transparent conical surface was carried out.
The author of work [12] has offered and developed a method of the solution of a
mathematical problem, to which the wave diffraction model problems for a solid semi-
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