Abstract
New solutions of the homogeneous wave equation of the type usually referred to as relatively undistorted waves are presented. Such solutions relate to the so-called splash modes, from which indeed they can be generated by applying the Laguerre polynomial operator. Accordingly, the solutions here presented resort to the relativistic Laguerre polynomials — introduced about one decade ago within a purely mathematical context — which in fact appear as modulating factor of the basic splash mode waveform. Similar solutions of the homogeneous spinor wave equation are also suggested.
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