Kerr型非线性介质层对波浪绕射的边值问题的可解性
Solvability of the boundary value problem associated with the wave diffraction by a layer filled with a Kerr-type nonlinear medium
摘要：
研究了平面波在横向非均匀各向同性双线性极化介质层中的衍射问题。分析和数值解技术的发展。将绕射问题归结为一个具有立方非线性项的二阶半线性常微分方程的奇异边值问题，然后再归结为一个第二类立方非线性积分方程和一个第二类非线性算子方程的迭代求解系统。利用压缩原理得到了该方程唯一可解的充分条件。
英文摘要：
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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