Geodesic
Renormalization group analysis for singularities in the wave beam self-focusing problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 119 (1999) no. 3, pp. 405-418

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A singular solution of the boundary value problem for the system of equations describing wave beam self-focusing is investigated by constructing renormalization group symmetries. New analytic expressions are found that characterize the spatial evolution of a beam with an arbitrary initial profile in a medium with cubic nonlinearity. The behavior of a Gaussian beam is thoroughly analyzed up to the moment the solution singularity is formed, and a hypothesis is proposed for describing the solution structure after the singularity occurs. 
@article{TMF_1999_119_3_a4,
     author = {V. F. Kovalev},
     title = {Renormalization group analysis for singularities in the wave beam self-focusing problem},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {405--418},
     publisher = {mathdoc},
     volume = {119},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_119_3_a4/}
}
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V. F. Kovalev. Renormalization group analysis for singularities in the wave beam self-focusing problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 119 (1999) no. 3, pp. 405-418. http://geodesic.mathdoc.fr/item/TMF_1999_119_3_a4/