Geodesic
Two-dimensional singular splash modes
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 79-84 
E. A. Zlobina; A. P. Kiselev. Two-dimensional singular splash modes. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 79-84. http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a5/
@article{ZNSL_2019_483_a5,
     author = {E. A. Zlobina and A. P. Kiselev},
     title = {Two-dimensional singular splash modes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {79--84},
     year = {2019},
     volume = {483},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a5/}
}
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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 specification of the 2D Bateman-type complexified solution with a singularity at a running point satisfies the homogeneous wave equation, while the respective non-complexified function does not.

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