Geodesic
Oscillating solitons of the~driven, damped nonlinear Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 536-544

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We obtain time-periodic solitons of the parametrically driven, damped nonlinear Schrödinger equation as solutions of the boundary value problem on a two-dimensional domain. We classify the stability and bifurcations of singly and doubly periodic solutions.
Keywords: nonlinear Schrödinger equation, parametric driving, stability, bifurcation of doubled period.
Mots-clés : Floquet multiplier 
@article{TMF_2009_159_3_a18,
     author = {E. V. Zemlyanaya and N. V. Alekseeva},
     title = {Oscillating solitons of the~driven, damped nonlinear {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {536--544},
     publisher = {mathdoc},
     volume = {159},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a18/}
}
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E. V. Zemlyanaya; N. V. Alekseeva. Oscillating solitons of the~driven, damped nonlinear Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 536-544. http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a18/