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Solvability of the boundary value problem associated with the wave diffraction by a layer filled with a Kerr-type nonlinear medium
Karlstad University, Faculty of Technology and Science, Department of Mathematics. (Surface Treatment Program/T2F)ORCID iD: 0000-0002-2691-2820
2009 (English)Report (Other academic)
Abstract [en]

The diffraction of a plane wave by a transversely inhomogeneousisotropic nonmagnetic linearly polarized dielectric layer filledwith a Kerr-type nonlinear medium is considered. The analyticaland numerical solution techniques are developed. The diffractionproblem is reduced to a singular boundary value problem for asemilinear second-order ordinary differential equation with acubic nonlinearity and then to a cubic-nonlinear integral equationof the second kind and to a system of nonlinear operatorequations of the second kind solved using iterations. Sufficientconditions of the unique solvability are obtained using the contraction principle

Place, publisher, year, edition, pages
ArXiv , 2009. , p. 22
Keywords [en]
nonlinear medium, cubic-nonlinear integral equation
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-11277OAI: oai:DiVA.org:kau-11277DiVA, id: diva2:494851
Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2016-06-09Bibliographically approved

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http://arxiv.org/abs/0910.2095

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Shestopalov, Youri
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