Non-propagating excitations in an infinite plane and three-dimensional medium

Abstract

Non-propagation is defined as the localization of excitations to the region, where the forcing density is applied. With this, it is aimed to find analogs of non-propagating string excitations into in a plane and 3-dimensional homogenous media. Assuming steady-state solutions and forcing densities, the Green's function of the inhomogenous wave equation was constructed being zero at the boundary where the forcing density is applied. Forcing densities, that were non-propagating, were argued to vanish in the immediate vicinity within the boundaries. An example of a non-propagating solution in a plane membrane was then showed proving their existence. The methods previously employed in the earlier parts of this paper were then extended to three dimensions.