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

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

2009-10-12

arxiv.org/abs/0910.2095v1

Mathematics

Analysis of PDEs

22 pages

Scientific paper

The diffraction of a plane wave by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The analytical and numerical solution techniques are developed. The diffraction problem is reduced to a singular boundary value problem for a semilinear second-order ordinary differential equation with a cubic nonlinearity and then to a cubic-nonlinear integral equation of the second kind and to a system of nonlinear operator equations of the second kind solved using iterations. Sufficient conditions of the unique solvability are obtained using the contraction principle.

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