An analytical-numerical computation of diffraction coefficients is described for a semi-infinite impedance cone circular cross section illuminated by an electromagnetic plane wave. To enable incomplete separation variables, both the incident and scattered fields are expressed in terms Kontorovich-Lebedev (KL) integrals; inversion Leontovich condition on cone's surface yields equations spectra, whose Fourier satisfy certain functional difference second order; latter then converted to integral...

We study electromagnetic plane wave diffraction by a hollow circular cone with thin walls modelled the so-called impedance-sheet boundary conditions. By means of Kontorovich–Lebedev integral representations for Debye potentials and ‘partial’ separation variables, problem is reduced to coupled functional difference (FD) equations relevant spectral functions. For cone, FD are then further equations, which subsequently shown be Fredholm-type via semi-inversion use Dixon's resolvent. solve...

This paper proposes an efficient solution procedure for second–order functional difference equations, and outlines this through investigating electromagnetic–wave diffraction by a canonical structure comprising impedance wedge sheet bisecting the exterior region of wedge. Applying Sommerfeld–Malyuzhinets technique to original boundary–value problem yields linear system equations two coupled spectral functions. Eliminating one function leads second-order equation other. The chief steps in...

This paper studies diffraction of an obliquely incident, arbitrarily polarized plane electromagnetic wave by anisotropic impedance wedge with opening angle 2/spl Phi/ between 0 and pi/, presents a closed-form exact solution to class faces the related uniform asymptotic (UAS). On use unitary similarity transform, boundary conditions on is brought into form, which makes exactly soluble evident. The found help Sommerfeld-Malyuzhinets (1896, 1958) technique, generalized Malyuzhinets function...

In this work, formal asymptotic solutions of a problem for linear water waves in bounded basin are constructed. The have the form quasimodes and used description standing localised near shoreline. Such short-wavelength exist only discrete set frequencies, which determined by means quantisation-type condition. Some numerical results also addressed.

This work studies functional difference equations of the second order with a potential belonging to special class meromorphic functions. The depend on spectral parameter. Consideration this type is motivated by applications in diffraction theory and construction eigenfunctions for Laplace operator angular domains. In particular, such describe eigenoscillations acoustic waves domains ‘semitransparent’ boundary conditions. For negative values parameter, we study essential discrete spectrum...

This paper consists of two parts and deals with the scattering wave-field generated by a Hertzian dipole placed over an impedance wedge. Expanding field into plane waves extending to complex “angles incidence” our recently obtained exact solution diffraction skew-incident wave wedge enables us give integral representation for total field. Then means asymptotic evaluation multiple far-field expressions are developed interpreted. In present first part (I) formulation basic steps analysis...

Eigenfunctions and their asymptotic behaviour at large distances for the Laplace operator with singular potential, support of which is on a circular conical surface in three-dimensional space, are studied. Within framework incomplete separation variables an integral representation Kontorovich–Lebedev (KL) type eigenfunctions obtained terms solution auxiliary functional difference equation meromorphic potential. Solutions studied by reducing it to bounded self-adjoint operator. To calculate...

An electromagnetic diffraction problem in a wedge shaped region is reduced to system of coupled functional equations by means Sommerfeld integrals. Anisotropic impedance boundary conditions are satisfied on the wedge's faces. This solved regular perturbation method. It shown that for weak anisotropy solution presented converging series which Neumann recurrent linear with contracting operators. In general case, compact The wave field asymptotic computed outside vicinity edge wedge.

This paper presents, as an extension of the authors' recent work, exact solution to diffraction a skew incident plane electromagnetic wave by wedge with axially anisotropic impedance faces. Applying Sommerfeld‐Malyuzhinets technique boundary‐value problem yields coupled system difference equations for spectra; on elimination, functional (FD) equation higher order one spectrum arises; after simplification in terms generalized Malyuzhinets function and accounting Meixner's edge condition well...

The problem of a plane wave diffraction by highly contrast transparent wedge an arbitrary opening is studied. With the aid Sommerfeld integrals it reduced to system coupled Maliuzhinets' equations. By use theory S-integrals functional equations transformed linear in Banach space. In case high material inside comparison with that wedge's exterior are solved means perturbation theory. Convergence corresponding Neumann series proved. Singularities integrands investigated. Application steepest...

The leading term for the scattering diagram, in scalar problem concerning diffraction of a plane wave by narrow circular impedance cone, is obtained. Although, up to now, cannot be solved an explicit form, its reduction non-oscillating integral equation has been recently developed. It used here order determine formal asymptotics diagram means perturbation method.