The Dirac-Delta Rogue Wave
arxiv(2024)
Abstract
This paper presents a double spatio-temporal localized Dirac-delta solution
for the linear wave equation. The solution arises from the interference of
sinusoidal waves with frequencies that vary as a function of the time of
emission. It is shown that the time-dependent frequency function required to
produce a localized Dirac-delta wave is exclusively determined by the
dispersion relation of the medium in which the wave is traveling. Both
numerical and exact analytical solutions for a typical physical scenario are
obtained and displayed. The application of this result to possible practical
uses is discussed.
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