Considering that classical electrodynamics is essentially a covariant theory, we propose a simple heuristic approach to nonlinear Maxwell equations where certain scalar fields are coupled to the electromagnetic (EM) field. This leads us to introduce a new (nonlinear) version of the Poynting theorem. This model seems to have solutions in which coupled scalar fields and EM waves propagate. This work could provide students with a first introduction to the basics of nonlinear electrodynamics within the framework of a new research problem. The content of this article is suitable for advanced graduate students in theoretical particle physics.

中文翻译：

---

非线性麦克斯韦方程和坡印廷定理

考虑到经典电动力学本质上是一种协变理论，我们对非线性麦克斯韦方程提出了一种简单的启发式方法，其中某些标量场与电磁 (EM) 场耦合。这导致我们引入新的（非线性）版本的坡印廷定理。该模型似乎具有耦合标量场和 EM 波传播的解决方案。这项工作可以在新研究问题的框架内为学生提供对非线性电动力学基础知识的首次介绍。本文内容适用于理论粒子物理高级研究生。