Abstract

A nonlinear eigenvalue problem on an interval is considered. The nonlinearity in the equation is specified by a nonnegative monotonically increasing function, and the boundary conditions nonlinearly depend both on the sought-for functions and on the spectral parameter. The discrete eigenvalues are defined using an additional (local) condition at one end of the interval. This problem describes the propagation of monochromatic (polarized) electromagnetic TM waves in a planar dielectric waveguide filled with a nonlinear medium. The nonlinearity covers a wide range of laws of nonlinear optics corresponding to self-interaction effects. Results on the solvability of the problem and the properties of the eigenvalues are obtained.

中文翻译：

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电磁波在充满非线性介质II：TM波的开放平面介质波导中的传播

摘要

考虑区间上的非线性特征值问题。方程中的非线性由一个非负的单调递增函数指定，边界条件非线性地取决于所寻求的函数和光谱参数。离散特征值是在间隔的一端使用附加（局部）条件定义的。这个问题描述了单色（极化）电磁TM波在充满非线性介质的平面介质波导中的传播。非线性涵盖了与自相互作用效应相对应的各种非线性光学定律。获得了问题可解性和特征值性质的结果。