skip to main content

SciTech ConnectSciTech Connect

Title: The fundamental solution of the unidirectional pulse propagation equation

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.
Authors:
 [1] ;  [2]
  1. Institute of Mathematics, Humboldt University, Rudower Chaussee 25, 12489 Berlin (Germany)
  2. CEA, DAM, DIF, F-91297 Arpajon (France)
Publication Date:
OSTI Identifier:
22251012
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; MATHEMATICAL SOLUTIONS; PULSES; WAVE EQUATIONS