Maxwell 方程的一个吸引人的解析解
An attractive analytic solution of the Maxwell's equation
AI总结：
本文提出了一种基于光滑周期函数的Maxwell方程解析解方法，其复杂度与傅里叶展开相当，并通过示例进行了验证。
摘要：
在本文中，我们为给定的一组光滑周期函数作为初始条件提供了Maxwell方程的吸引人的解析解，并提供了示例。该解的复杂性与初始函数的傅里叶展开相当。
英文摘要：
In this paper, we aim to develop a closed-form solution of the standard Maxwell's equations that describe the propagation of electromagnetic waves in an isotropic homogeneous medium such as a vacuum. The proposed solution has a simple analytic structure that explains how initial conditions characterize the underlying electromagnetic wave. As such, it can be used as a tool to generate suitable electromagnetic waves in practice. The clean structure of the solution can also help us to derive closed-form solutions in a general medium with a non-zero current term. In this paper, we enhance the solution to cover a special case where the current comes from the contribution of an independent generator. We shall leverage the tools developed in this paper to derive similar closed-form solutions of Maxwell's equations in general mediums with non-zero currents in a separate paper.
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