Analysis shows fractional dispersion in Helmholtz equation solutions with periodic scattering data, suggesting behaviors align with those of the Schrödinger equation.
We investigate the fractional dispersion of solutions to the Helmholtz equation with periodic scattering data. We show that, under appropriate rescaling, the interaction between the different frequencies exhibits the same fluctuating behavior as for the Schr\"{o}dinger equation. To achieve this, we first establish an asymptotic fractional uncertainty principle for solutions to the Helmholtz equation.
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Canto et al. (2025) studied this question.
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