The Propagation of Electromagnetic Waves Through, Along and Over a Three-Dimensional Conducting Half Space: EM Waves Over a Conducting Earth (Methoden und Verfahren der mathematischen Physik) - Softcover

Gilliam, D.S.; Schulenberg, John R.

Softcover

ISBN 10: 3820489053 ISBN 13: 9783820489057

Publisher: Peter Lang GmbH, Internationaler Verlag der Wissenschaften, 1986

Synopsis

A representation in terms of explicitly given generalized eigenfunctions is obtained for the semigroup S(t) = exp(-ixt) solving the Cauchy problem for the time-dependent Maxwell equations in the case of two distinct media filling the upper and lower half spaces of R3, whereby the upper medium is loss-free, while the lower has finite conductivity. The solution u = S(t)f, fED(1), can be written in the form u = uo+uo+uso+us++us-+op+up. Here uo and uo are, respectively, static and quasistatic parts of the solution: us+ and us+ consists of a superposition of AH modes -- modes whose frequencies have no real part and thus do not propagate; uxx consist of superpositions of surface-wave modes, propagating in opposite directions according to + or -; uop and up are superpositions of plane-wave modes having the frequencies of the upper and lower media respectively. The structure of the AH and surface-wave components is determined: the are essentially scalar waves, and it is shown how such waves can be constructed explicitly from solutions of a simple problem for the scalar wave equation.

About this title

Review:

«This monograph ... should be highly appreciated by applied mathematicians and mathematical physicists interested in electromagnetic (and other) wave propagation phenomena.» (Rainer Picard, Mathematical Reviews)

About this edition

• Publisher: Peter Lang GmbH, Internationaler Verlag der Wissenschaften
• Publication date: 1986
• ISBN 10: 3820489053
• ISBN 13: 9783820489057
• Binding: Paperback
• Number of pages: 209