Geodesic
Singular astigmatic splash pulse is a solution of the homogeneous wave equation
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 53, Tome 521 (2023), pp. 54-58

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It is proved that a certain simple Bateman-type function having a running singularity, satisfies the homogeneous wave equation on the entire space-time. 
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     author = {I. A. Blagoveshchenskii and A. P. Kiselev},
     title = {Singular astigmatic splash pulse is a solution of the homogeneous wave equation},
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I. A. Blagoveshchenskii; A. P. Kiselev. Singular astigmatic splash pulse is a solution of the homogeneous wave equation. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 53, Tome 521 (2023), pp. 54-58. http://geodesic.mathdoc.fr/item/ZNSL_2023_521_a3/