Abstract

An application of the integral dispersion equation method to the solution of two nonlinear eigenvalue problems is considered. One of these problems arises when studying the propagation of TE-waves in a dielectric shielded nonlinear layer with Kerr nonlinearity, while the other, a more complex one, generalizes the first and contains, in particular, a nonlinearity multiplying the highest derivative in the differential operator. The existence of an infinite set of eigenvalues of the problems is proved, and their asymptotics is found.

中文翻译：

---

非线性特征值问题的积分色散方程法

摘要

考虑了积分色散方程法在求解两个非线性特征值问题中的应用。研究TE波在具有Kerr非线性的介电屏蔽非线性层中的传播时，会出现这些问题，而另一个更为复杂的问题则是将第一个广义化，尤其是包含将微分中的最高导数相乘的非线性。操作员。证明了问题的无穷特征值的存在，并找到了它们的渐近性。