After critical and precritical bifurcations of progressive wave in a generalized Ginzburg–Landau equation
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2009), pp. 71-78 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A generalized time dependent Ginzburg–Landau equation is considered with periodic boundary conditions. There is contable number progressive wave. Local bifurcations of that solutions is edudied when they change the stability. The torus of the $2$ dimension bifurcate of each of the progressive wave. In particular, the possibility of precritic hard bifurcation is demonstrated for this equations.
Keywords: stability, soft and hard bifurcations
Mots-clés : invariant torus.
@article{VUU_2009_4_a6,
     author = {A. N. Kulikov and D. A. Kulikov},
     title = {After critical and precritical bifurcations of progressive wave in a~generalized {Ginzburg{\textendash}Landau} equation},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {71--78},
     year = {2009},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2009_4_a6/}
}
TY  - JOUR
AU  - A. N. Kulikov
AU  - D. A. Kulikov
TI  - After critical and precritical bifurcations of progressive wave in a generalized Ginzburg–Landau equation
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2009
SP  - 71
EP  - 78
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VUU_2009_4_a6/
LA  - ru
ID  - VUU_2009_4_a6
ER  - 
%0 Journal Article
%A A. N. Kulikov
%A D. A. Kulikov
%T After critical and precritical bifurcations of progressive wave in a generalized Ginzburg–Landau equation
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2009
%P 71-78
%N 4
%U http://geodesic.mathdoc.fr/item/VUU_2009_4_a6/
%G ru
%F VUU_2009_4_a6
A. N. Kulikov; D. A. Kulikov. After critical and precritical bifurcations of progressive wave in a generalized Ginzburg–Landau equation. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2009), pp. 71-78. http://geodesic.mathdoc.fr/item/VUU_2009_4_a6/

[1] Drazin F., Vvedenie v teoriyu gidrodinamicheskoi ustoichivosti, Fizmatlit, M., 2005, 287 pp.

[2] Scheuer J., Malomed B. A., “Stable and chaotic solutions of the Ginzburg–Landau equation with periodic boundary conditions”, Physika D, 161:1–2 (2002), 102–115 | DOI | Zbl

[3] Malinetskii G. G., Potapov A. B., Podlazov A. V., Nelineinaya dinamika, Izd-vo Komkniga, M., 2006, 280 pp.

[4] Deissler R. J., “Turbulent burth, spots and slugs in a generalized Ginzburg–Landau equation”, Physics Letters A, 120:7 (1987), 334–340 | DOI | MR

[5] Yakubov S. Ya., “Razreshimost zadachi Koshi dlya abstraktnykh uravnenii vtorogo poryadka i ikh prilozheniya”, Trudy MMO, 27, 1970, 37–59

[6] Khessard B., Kazarinov N., Ven I., Teoriya i prilozheniya bifurkatsii rozhdeniya tsikla, Mir, M., 1985, 280 pp. | MR

[7] Kulikov A. N., Kulikov D. A., “Bifurkatsiya kubicheskogo uravneniya Shredingera v sluchae trekh nezavisimykh peremennykh”, Vestnik Udmurtskogo universiteta, 2008, no. 3, 23–34

[8] Kotikov A. E., Kulikov A. N., “Bifurkatsiya beguschikh voln vidoizmennogo uravneniya Ginzburga–Landau”, Modelir. i analiz inform. sistem, 15:1 (2008), 10–15 | MR

[9] Kolesov A. Yu., Kulikov A. N., Rozov N. Kh., “Tsilindricheskie beguschie volny obobschennogo kubicheskogo uravneniya Shredingera”, Doklady RAN, 73:1 (2006), 125–129

[10] Demidovich B. P., Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967, 472 pp. | MR

[11] Marsden Dzh., Mak-Kraken M., Bifurkatsiya rozhdeniya tsikla i ee prilozheniya, Mir, M., 1980, 369 pp. | MR | Zbl

[12] Kolesov A. Yu., Kulikov A. N., Invariantnye tory nelineinykh evolyutsionnykh uravnenii, YarGU, Yaroslavl, 2003, 107 pp.

[13] Kolesov A. Yu., Kulikov A. N., Rozov N. Kh., “Invariantnye tory odnogo klassa tochechnykh otobrazhenii: printsip koltsa”, Diff. uravn., 39:5 (2003), 584–601 | MR | Zbl

[14] Kolesov A. Yu., Kulikov A. N., Rozov N. Kh., “Invariantnye tory odnogo klassa tochechnykh otobrazhenii: sokhranenie invariantnogo tora pri vozmuscheniyakh”, Diff. uravn., 39:6 (2003), 738–753 | MR | Zbl