Plane Waves, Bateman’s Solutions, and Sources at Infinity

详细

For the three-dimensional 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 is obtained by application of the Kelvin–Bateman transformation to a plane wave) is a solution of the wave equation everywhere in ℝ⁴. Bibliography: 5 titles.