Solvability of the boundary value problem associated with the wave diffraction by a layer filled with a Kerr-type nonlinear medium

摘要

The diffraction of a plane wave by a transversely inhomogeneous isotropicnonmagnetic linearly polarized dielectric layer filled with a Kerr-typenonlinear medium is considered. The analytical and numerical solutiontechniques are developed. The diffraction problem is reduced to a singularboundary value problem for a semilinear second-order ordinary differentialequation with a cubic nonlinearity and then to a cubic-nonlinear integralequation of the second kind and to a system of nonlinear operator equations ofthe second kind solved using iterations. Sufficient conditions of the uniquesolvability are obtained using the contraction principle.