Generalized theory of normal waves in layered media

Using the example of the Pekeris waveguide, we show that boundary value problems for a layered half-space in the classical setting are ill-posed. One of the solutions of the reduced Pekeris boundary value problem is suggested, which satisfies the generalized radiation condition on the impedance interface. The mode part of this solution is represented by the expansion in the complete system of normal waves, including regular, generalized, and leaky waves. We construct an extension of the solution to the half-space in the class of generalized functions satisfying the quenching condition at infinity. Foundations of the generalized theory are formulated. Peculiarities of the generalized theory as compared to the classical theory are analyzed.