Geodesic
On the nonlinear analogue of the WCB method and the method of the averaged lagrangian
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 12, Tome 117 (1981), pp. 162-171

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The article concerns some relations between the annouced methods. 
@article{ZNSL_1981_117_a10,
     author = {Ya. V. Kurylev},
     title = {On the nonlinear analogue of the {WCB} method and the method of the averaged lagrangian},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {162--171},
     publisher = {mathdoc},
     volume = {117},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_117_a10/}
}
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Ya. V. Kurylev. On the nonlinear analogue of the WCB method and the method of the averaged lagrangian. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 12, Tome 117 (1981), pp. 162-171. http://geodesic.mathdoc.fr/item/ZNSL_1981_117_a10/