The retarded potential of a non-homogeneous wave equation: introductory analysis through the Green Functions

Authors

  • A. Téllez-Quiñones CONACYT-Centro de Investigación en Geografía y Geomática (Unidad Mérida)
  • J. C. Valdiviezo-Navarro CONACYT-Centro de Investigación en Geografía y Geomática (Unidad Mérida)
  • A. Salazar-Garibay CONACYT-Centro de Investigación en Geografía y Geomática (Unidad Mérida)
  • A. A. López Caloca Centro de Investigación en Geografía y Geomática

DOI:

https://doi.org/10.31349/RevMexFisE.64.26

Keywords:

Mathematical methods in physics, mathematics, diffraction theory, backscattering, radar.

Abstract

The retarded potential, a solution of the non-homogeneous wave equation, is a subject of particular interest in many physics and engineering applications. Examples of such applications may be the problem of solving the wave equation involved in the emission and reception of a signal in a synthetic aperture radar (SAR), scattering and backscattering, and general electrodynamics for media free of magnetic charges.
However, the construction of this potential solution is based on the theory of  distributions, a topic that requires special care and time to be understood with mathematical rigor. Thus, the goal of this study is to provide an introductory analysis, with a medium level of formalism, on the construction of this potential solution and the handling of Green functions represented by sequences of well-behaved approximating
functions.

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Published

2018-04-10