Fermat's principle for dispersive waves in nonstationary media

Fermat's principle is extended to nonstationary, anisotropic, inhomogeneous media that support a class of waves with frequency-dependent velocity. The approach used to prove the stationarity of travel times with respect to deformation of the actual ray trajectory is based on a comparison of the rays that follow from the variational principle, and from the eikonal equation. The identities that relate phase and group velocities and their derivatives in rather general anisotropic, dispersive, inhomogeneous, nonstationary media are established, it is shown that not only the travel time, but the optical path length as well, is stationary on the actual ray in media with time-dependent parameters if wave frequency is required to be the same function of time on every trial ray as it is on the actual ray