Abstract
The ray description in the WKB (or eikonal) limit is extended to all orders in the expansion in powers of wavelength/characteristic length. The equations for the ray trajectories are given by a Hamiltonian system, and the intensity is given by a conservation law with flow along the rays, just as in the eikonal limit. The generalization requires that the Hamiltonian depends weakly on the solution, in a way which can be solved iteratively.
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