We consider propagation of surface Transverse Electric (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 surface 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表面波

我们考虑在充满非线性超材料介质的杆中传播表面横波（TE）。将该问题简化为带有核的非线性积分方程的分析，其形式为区间上辅助边值问题的格林函数。利用收缩方法证明了对于选择的非线性（Kerr定律）传播的非线性表面TE波的存在。对于数值解，提出了一种基于解决辅助柯西问题的方法（射击方法的一种形式）。发现了新的传播方式。