The Pekeris waveguide: A case study in classical applied mathematics

In this paper various mathematical models for underwater acoustic wave propagation are reviewed and summarized. The primary model is the Pekeris waveguide, and this is used as a case study by incorporating many related mathematical methods in a single context. Often such methods are perceived by graduates in a compartmentalized fashion, and rarely, without artificiality, is it possible to utilize more than a few such techniques to gain deeper insight into a physical problem. In addition, (i) a continuously-stratified problem, (ii) a related inverse problem and (iii) a non-self-adjoint problem associated with a lossy waveguide are discussed in the light of results from the basic two-layer model. Three appendices briefly address more technical aspects of the associated governing differential equations.