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 
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/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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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