Progress and Prospects in the Theory of Linear Wave Propagation

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Abstract
The development of the theory of linear wave propagation is described after a brief sketch of what wave propagation is. First the classical techniques of images and separation of variables are considered, followed by Sommerfeld’s extension of the image method to multi-sheeted spaces, and Watson’s transformation of series solutions to more rapidly converging forms. Then the Wiener–Hopf method of solving certain integral equations and Schwinger’s variational method of calculating scattering parameters are introduced. Next the normal mode theory of propagation and its development by Pekeris, Fock, Brekhovskikh and others is described. Then the WKB method and its extensions are presented. This is followed by discussions of ray theory, of the “parabolic equation” method, and of waves in heterogeneous and random media. Finally prospects for the future are considered, with emphasis on the use of computers and methods of calculation.

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