Modern Developments in Asymptotic Ray Theory

Ray methods applied to the Helmholtz equation have been developed for, and applied to, high-frequency diffraction and scattering problems with unparalleled success. This theory underpins mathematical optics and is fundamental to the geometrical theory of diffraction. It relies upon describing waves in terms of an amplitude expansion and a single phase term, from which partial differential equations for these quantities follow.
The lead investigator has identified a novel class of topical problems for which this approach does not work, and the plan is to modify substantially the existing theory by the inclusion of a generalised sum of terms in the phase, and then to apply the newly generalised theory to these problems.