Abstract
We consider two classes of exact solutions of the wave equation, which play an important role in the linear theory of localized wave propagation. These are the complexified spherical wave, known as the “complex source wavefield”, and the complexified Bateman solution. Both involve an arbitrary analytic function of a complex argument, known as the waveform. We explore a possibility of considering non-analytical waveforms and establish that in the both cases the analyticity is unavoidable.
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