Geodesic
Gaussian beams, the Hamilton--Jacobi equations and Finsler geometry
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 66-92

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The relationships between Gaussian beams and geometry are considered in the paper. It is shown that the main properties of the Gaussian beam solutions are determined by the natural geometry, related to the problem under considerations. The geometry is determined by the Hamilton–Jacobi equation and corresponding hamiltonian. In particular, it was found a geometric interpretation of the Riccati equation for the quadratic form of the phase function corresponding to the Gaussian beam in the case of Finsler geometry. 
@article{ZNSL_2003_297_a4,
     author = {A. P. Katchalov},
     title = {Gaussian beams, the {Hamilton--Jacobi} equations and {Finsler} geometry},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {66--92},
     publisher = {mathdoc},
     volume = {297},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a4/}
}
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A. P. Katchalov. Gaussian beams, the Hamilton--Jacobi equations and Finsler geometry. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 66-92. http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a4/