The deferred limit method for long waves in a curved waveguide

This paper presents a technique, based on a deferred approach to a limit, for analysing the dispersion relation for propagation of long waves in a curved waveguide. The technique involves the concept of an analytically satisfactory pair of Bessel functions, which is different from the concept of a numerically satisfactory pair, and simplifies the dispersion relations for curved waveguide problems. Details are presented for long elastic waves in a curved layer, for which symmetric and antisymmetric waves are strongly coupled. The technique gives high-order corrections to a widely used approximate dispersion relation based a kinematic hypothesis, and determines rigorously which of its coefficients are exact.