单向脉冲传播方程的基本解
The fundamental solution of the unidirectional pulse propagation equation
摘要：
得到了三维波动方程的一种变形形式“单向脉冲传播方程”（UPPE）及其傍轴近似的基本解。它表明，基本解可以表示为一个投影的基本解的波动方程的功能子空间。我们讨论了UPPE和波动方程在这方面的等价度。特别是，我们表明，UPPE，在相反的共同信念，描述波在纵向和时间方向的传播，因此，它的基本解决方案具有非因果性质。
英文摘要：
The fundamental solution of a variant of the three-dimensional wave equation known as "unidirectional pulse propagation equation" (UPPE) and its paraxial approximation is obtained. It is shown that the fundamental solution can be presented as a projection of a fundamental solution of the wave equation to some functional subspace. We discuss the degree of equivalence of the UPPE and the wave equation in this respect. In particular, we show that the UPPE, in contrast to the common belief, describes wave propagation in both longitudinal and temporal directions, and, thereby, its fundamental solution possesses a non-causal character.
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