WIAS Preprint No. 1808, (2013)

The fundamental solution of unidirectional pulse propagation equation



Authors

  • Babushkin, Ihar

2010 Mathematics Subject Classification

  • 78A60 35Q61 35Q60

Keywords

  • fundamental solution, unidirectional pulse propagating equation

Abstract

In the article the fundamental solution of a variant of 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 UPPE and wave equation in this respect. In particular, we show that UPPE, in contrast to the widespread belief, describes the wave propagation in both directions simultaneously, and remark non-causal character of its solutions.

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