Plane waves, Batmen's solutions and sources at infinity
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 23-33
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For threedimensional wave equation two equivalent statements are proved:
1) plane waves are not generated by a source at infinity,
2) Bateman's solution (the solution that obtained by the application of Kelvin–Bateman transformation to a plane wave) is the solution to wave equation everywhere in $\mathbb R^4$.
@article{ZNSL_2014_426_a3,
author = {A. S. Blagovestchensky},
title = {Plane waves, {Batmen's} solutions and sources at infinity},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {23--33},
publisher = {mathdoc},
volume = {426},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a3/}
}
A. S. Blagovestchensky. Plane waves, Batmen's solutions and sources at infinity. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 23-33. http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a3/