Geodesic
Bifurcation of autowaves of generalized cubic Schr\"odinger equation with three independent variables
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2008), pp. 23-34

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Periodic boundary value problem the name of which is given in the title of this article is considered in this work. There is a countable number of plane waves which are periodic on according to time variable. The question of their stability and bifurcation has been examined. Each of them turned out to bifurcate invariant tors of $2,\,3,\,4$ dimensions, including asymptotically stable ones. Features which make them different from the analogous problem when the number of space variables equals $1$ or $2$ are also shown. In particular we have shown parameter ranges when precritic bifurcation of saddle tors is possible and revealed the cases of realization of stable regimes with sharpening the latter is illustrated by figures. All these results have been obtained analytically and are based on asymptotic methods of nonlinear dynamic.
Keywords: attractor, nonlinear boundary value problems.
Mots-clés : bifurcation 
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     author = {A. N. Kulikov and D. A. Kulikov},
     title = {Bifurcation of autowaves of generalized cubic {Schr\"odinger} equation with three independent variables},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {23--34},
     publisher = {mathdoc},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2008_3_a2/}
}
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A. N. Kulikov; D. A. Kulikov. Bifurcation of autowaves of generalized cubic Schr\"odinger equation with three independent variables. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2008), pp. 23-34. http://geodesic.mathdoc.fr/item/VUU_2008_3_a2/