Abstract
We study the d’Alembert equation with a boundary. We introduce the notions of Rayleigh surface wave operators, delayed/advanced mirror images, wave recombinations, and wave cancellations. This allows us to obtain the complete and simple formula of the Green’s functions for the wave equation with the presence of various boundary conditions. We are able to determine whether a Rayleigh surface wave is active or virtual, and study the lacunas of the wave equation in three dimensional with the presence of a boundary in the case of a virtual Rayleigh surface wave.
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Deng, S., Wang, W. & Yu, SH. Green’s Functions of Wave Equations in \(\mathbb{R}^n_+\times \mathbb{R}_+\) . Arch Rational Mech Anal 216, 881–903 (2015). https://doi.org/10.1007/s00205-014-0821-2
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DOI: https://doi.org/10.1007/s00205-014-0821-2