The fundamental solution of the unidirectional pulse propagation equation

10Citations
Citations of this article
12Readers
Mendeley users who have this article in their library.

Abstract

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. © 2014 AIP Publishing LLC.

Cite

CITATION STYLE

APA

Babushkin, I., & Bergé, L. (2014). The fundamental solution of the unidirectional pulse propagation equation. Journal of Mathematical Physics, 55(3). https://doi.org/10.1063/1.4868698

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free