Geodesic
On the Bateman--H\"ormander solution of the wave equation, having a~singularity at a~running point
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 76-85

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Hörmander have presented a remarkable example of a solution of the homogeneous wave equation, which has a singularity at a running point. We are concerned with analytic investigation of this solution for the case of three spatial variables. We describe its support, study its behavior near the singular point and establish its local integrability. We observe that the Hörmander solution is a specialization of a solution found by Bateman five decades in advance. 
@article{ZNSL_2018_471_a4,
     author = {A. S. Blagoveshchensky and A. M. Tagirdzhanov and A. P. Kiselev},
     title = {On the {Bateman--H\"ormander} solution of the wave equation, having a~singularity at a~running point},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {76--85},
     publisher = {mathdoc},
     volume = {471},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a4/}
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A. S. Blagoveshchensky; A. M. Tagirdzhanov; A. P. Kiselev. On the Bateman--H\"ormander solution of the wave equation, having a~singularity at a~running point. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 76-85. http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a4/