Energy flux for trains of inhomogeneous plane waves

The propagation of inhomogeneous plane waves in linear conservative systems is considered. It is assumed that the secular equation governing the propagation of a plane wave of slowness S has the form Q(S) = 0 where Q is independent of frequency. Dispersion enters via the boundary conditions. By using the point form of the conservation of energy equation results are obtained which relate the mean energy flux vector R˜ with the mean energy density Ẽ for any number of wave trains. In particular for a single train of inhomogeneous plane waves it is shown that R˜.S+ = Ẽ. The results are relevant in electromagnetism, elasticity and fluid dynamics.