Abstract
Although invariant imbedding techniques have been successfully applied to various one-dimensional wave-propagation problems [2–5, 7, 11], until now little has been done to extend these techniques to wave propagation in more than one dimension. It might, at first glance, appear that the recent work of Angel, Jain, and Kalaba [1], on the two-dimensional Laplace equation could easily be extended to the slightly more complicated two-dimensional reduced wave equation. However, this turns out to not be the case for our problem since the boundary conditions are of a different nature.
Supported by the National Science Foundation under Grant No. GP 20423 and the Atomic Energy Commission under Grant No. At-11–1–1113, Project #19.
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References
Angel, E., A. Jain, and R. Kalaba, “Initial-Value Problems in Potential Theory,” University of Southern California TR-70–22, April 1970.
Atkinson, F., “Wave Propagation and the Bremmer Series,” J. Math. Anal. and Appl. 1, 255–276, I960.
Bellman, R., and R. Kalaba, “Functional Equations, Wave Propagation, and Invariant Imbedding,” J. of Math. and Mechanics, 8, 683–704, 1959.
Bellman, R., and R. Kalaba, “Invariant Imbedding and Wave Propagation in Stochastic Media, “Electromagnetic Wave Propagation, “Academic Press, New York, pp. 243–252, 1960.
Bellman, R., and R. Kalaba, “Wave Branching Processes and Invariant Imbedding, I,” Proc. Nat. Acad. Sci., 47, 1507–1509, 1961.
Born, M., and E. Wolf, Principles of Optic, Pergamon Press New York, 1959.
Kalaba, R., “Boundary-Value Problems for the Integro-Differential Equations of Nonlocal Wave Interaction: I,” J. Math. Phys., 11, 1999–2004, 1970.
Kline, M., Editor, The Theory of Electromagnetic Waves, Inter science, New York, 1951, Dover, New York, 1965.
Lehman, G., “Diffraction of Electromagnetic Waves by Planer Dielectric Structures: I, Transverse Electric Excitation,” J. Math. Phys. 11, 1522–1535, 1970.
Noble, B., Wiener-Hopf Techniques, Pergamon Press New York, 1958.
Wilcox, R., “Transmission of Electromagnetic Wave through a Conducting Plasma Stab,” University of Southern California TR-70–34, June 1970.
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Wilcox, R. (1971). Wave Propagation through Longitudinally and Transversally Inhomogeneous Slabs-I. In: Bellman, R.E., Denman, E.D. (eds) Invariant Imbedding. Lecture Notes in Operations Research and Mathematical Systems, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46274-0_7
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DOI: https://doi.org/10.1007/978-3-642-46274-0_7
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