Abstract

We describe the application of the phase plane method to analyze the behavior of stationary harmonic plane electromagnetic waves. The phase plane method allows one to describe qualitatively all possible solutions of the Helmholtz nonlinear differential equation without performing a numerical integration. All types of phase portraits for waves in the media with self-action are presented and their physical interpretation is discussed. The consideration is carried out on the model of cubic nonlinearity without specifying the physical mechanism of this nonlinearity. The features of the nonlinear case are discussed. The phenomenon of the self-limitation of the transmitted wave power in a medium with negative nonlinearity is described.

中文翻译：

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具有自作用的介质中电磁波的亥姆霍兹方程解的相平面分析

摘要

我们描述了相平面方法在分析平稳谐波平面电磁波行为中的应用。相平面法可以定性地描述亥姆霍兹非线性微分方程的所有可能解，而无需进行数值积分。介绍了具有自作用的介质中波的所有类型的相像，并讨论了它们的物理解释。对立方非线性模型进行了考虑，但未指定这种非线性的物理机制。讨论了非线性情况的特征。描述了具有负非线性的介质中传输波功率的自限制现象。