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

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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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     author = {E. A. Zlobina and A. P. Kiselev},
     title = {Two-dimensional singular splash modes},
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     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a5/}
}
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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/