Journal
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
Volume 59, Issue 6, Pages 958-977Publisher
PLEIADES PUBLISHING INC
DOI: 10.1134/S0965542519060137
Keywords
Maxwell's equations; nonlinear eigenvalue problem; nonlinear Sturm-Liouville problem; asymptotics of eigenvalues; comparison theorem; planar dielectric waveguide; nonlinear permittivity
Categories
Funding
- Russian Science Foundation [18-71-10015]
- Russian Science Foundation [18-71-10015] Funding Source: Russian Science Foundation
Ask authors/readers for more resources
A nonlinear Sturm-Liouville-type eigenvalue problem on an interval with the boundary conditions of the third kind and an additional (local) condition at one of the ends of the interval is studied. The nonlinearity in the equation is specified by a nonnegative monotonically increasing function, and the boundary conditions depend nonlinearly on the spectral parameter. Such a problem describes the propagation of monochromatic electromagnetic TE waves in a planar dielectric waveguide filled with a nonlinear medium. The nonlinearity function covers a wide range of laws of nonlinear optics corresponding to the self-action effects. Results on the solvability of the problem and the properties of eigenvalues are obtained.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available