Acoustic and Electromagnetic Bullets: Derivation of New Exact Solutions of the Acoustic and Maxwell's Equations

Previously it has been shown that all finite energy, causal solutions of the time-dependent three-dimensional acoustic equation and Maxwell's equations have forms for large radius that, except for a factor 1/r, represent one-dimensional wave motions along straight lines through the origin. The...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 1990-10, Vol.50 (5), p.1325-1340
Main Authors: Moses, Harry E., Prosser, Reese T.
Format: Article
Language:English
Subjects:
Acoustics
Bullets
Cartesianism
Electric fields
Electromagnetism
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Hemispheres
Magnetic fields
Mathematical functions
Maxwell equations
Physics
Radon
Sine function
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Summary:Previously it has been shown that all finite energy, causal solutions of the time-dependent three-dimensional acoustic equation and Maxwell's equations have forms for large radius that, except for a factor 1/r, represent one-dimensional wave motions along straight lines through the origin. The asymptotic region is called the wave zone. Conversely, it also has been shown how the exact finite energy causal solutions can be obtained from the asymptotic solutions in the wave zone through the use of a refined Radon transform. Thus a way of finding exact, causal three-dimensional solutions from the essentially one-dimensional solutions in the wave zone has been obtained. When the asymptotic solutions are confined to a finite radial interval within a cone, the exact solutions are termed "bullets" and asymptotically represent packets of acoustic and electromagnetic energy "shot" through the cone, which is a kind of "rifle." No reflectors are needed. In the present paper explicit examples of such exact solutions are derived.
ISSN:0036-1399
1095-712X
DOI:10.1137/0150079