Geodesic
Renormgroup symmetries in problems of nonlinear geometrical optics
Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 3, pp. 369-388

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Renormgroup symmetries for a boundary value problem for the system of equations which describes propagation of a powerful radiation in a nonlinear medium in geometrical optics approximation are constructed. With the help of renormgroup symmetries new exact and approximate analytical solutions of nonlinear geometrical optics equations are obtained. Explicit analytical expressions are presented that characterize spatial evolution of a laser beam which has an arbitrary intensity dependence at the boundary of the nonlinear medium. 
@article{TMF_1997_111_3_a4,
     author = {V. F. Kovalev},
     title = {Renormgroup symmetries in problems of nonlinear geometrical optics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {369--388},
     publisher = {mathdoc},
     volume = {111},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_111_3_a4/}
}
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V. F. Kovalev. Renormgroup symmetries in problems of nonlinear geometrical optics. Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 3, pp. 369-388. http://geodesic.mathdoc.fr/item/TMF_1997_111_3_a4/