We consider propagation of leaky TE waves in a rod filled with nonlinear metamaterial medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky TE waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. New propagation regimes are discovered.

中文翻译：

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非线性超材料棒中的漏波

我们考虑在充满非线性超材料介质的杆中传播泄漏的 TE 波。该问题被简化为分析具有核的非线性积分方程，该方程为区间上辅助边值问题的格林函数形式。使用收缩方法证明了所选非线性（克尔定律）的传播非线性泄漏 TE 波的存在。对于数值解，提出了一种基于求解辅助柯西问题的方法（射击法的一个版本）。发现了新的传播机制。