TY - JOUR

T1 - Integral Equations and the Scattering Diagram in the Problem of Diffraction by Two Shifted Contacting Wedges with Polygonal Boundary

AU - Lyalinov, M.A.

N1 - Lyalinov, M.A. Integral Equations and the Scattering Diagram in the Problem of Diffraction by Two Shifted Contacting Wedges with Polygonal Boundary. J Math Sci 214, 322–336 (2016). https://doi.org/10.1007/s10958-016-2780-7

PY - 2016

Y1 - 2016

N2 - The acoustic problem of diffraction by two wedges with different wave velocities is studied. It is assumed that the wedges with parallel edges have a common part of the boundary and the second wedge is shifted with respect of the first one in the orthogonal to the edges direction along the common part of the boundary. The wave field is governed by the Helmholtz equations. On the polygonal boundary, separating these shifted wedges from the exterior, the Dirichlet boundary condition is satisfied. The wave field is excited by an infinite filamentary source, which is parallel to the edges. In these conditions, the problem is effectively two-dimensional. The Kontorovich–Lebedev transform is applied to separate the radial and angular variables and to reduce the problem at hand to integral equations of the second kind for so-called spectral functions. The kernel of the integral equations given in the form of an integral of the product of Macdonald functions is analytically transformed to a simplified expression. For

AB - The acoustic problem of diffraction by two wedges with different wave velocities is studied. It is assumed that the wedges with parallel edges have a common part of the boundary and the second wedge is shifted with respect of the first one in the orthogonal to the edges direction along the common part of the boundary. The wave field is governed by the Helmholtz equations. On the polygonal boundary, separating these shifted wedges from the exterior, the Dirichlet boundary condition is satisfied. The wave field is excited by an infinite filamentary source, which is parallel to the edges. In these conditions, the problem is effectively two-dimensional. The Kontorovich–Lebedev transform is applied to separate the radial and angular variables and to reduce the problem at hand to integral equations of the second kind for so-called spectral functions. The kernel of the integral equations given in the form of an integral of the product of Macdonald functions is analytically transformed to a simplified expression. For

KW - spectral functions

KW - Singular Integral Equation

KW - Cylindrical Wave

KW - Fredholm Property

KW - Polygonal Boundary

U2 - 10.1007/s10958-016-2780-7

DO - 10.1007/s10958-016-2780-7

M3 - Article

VL - 214

SP - 322

EP - 336

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -