Geodesic
Bifurcations of homogeneous cycle of generalized cubic Shrodinger equation in the triangle
Modelirovanie i analiz informacionnyh sistem, Tome 15 (2008) no. 2, pp. 50-54.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the generalized cubic Scrodinger equation in rectangular equilateral triangle provided that solution satisfies the homogeneous Neumann boundary condition. Stability and local bifurcations of homogeneous cycle are studied. We show that the bifurcation of two nonhomogeneous cycles takes place when homogeneous cycle loses its stability. 
@article{MAIS_2008_15_2_a7,
     author = {D. A. Kulikov},
     title = {Bifurcations of homogeneous cycle of generalized cubic {Shrodinger} equation in the triangle},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {50--54},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2008_15_2_a7/}
}
TY  - JOUR
AU  - D. A. Kulikov
TI  - Bifurcations of homogeneous cycle of generalized cubic Shrodinger equation in the triangle
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2008
SP  - 50
EP  - 54
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2008_15_2_a7/
LA  - ru
ID  - MAIS_2008_15_2_a7
ER  - 
%0 Journal Article
%A D. A. Kulikov
%T Bifurcations of homogeneous cycle of generalized cubic Shrodinger equation in the triangle
%J Modelirovanie i analiz informacionnyh sistem
%D 2008
%P 50-54
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2008_15_2_a7/
%G ru
%F MAIS_2008_15_2_a7
D. A. Kulikov. Bifurcations of homogeneous cycle of generalized cubic Shrodinger equation in the triangle. Modelirovanie i analiz informacionnyh sistem, Tome 15 (2008) no. 2, pp. 50-54. http://geodesic.mathdoc.fr/item/MAIS_2008_15_2_a7/

[1] E. Skott, Volny v aktivnykh i nelineinykh sredakh v prilozhenii k elektrodinamike, Sovetskoe radio, M., 1977, 368 pp.

[2] Dzh. Uizem, Lineinye i nelineinye volny, Mir, M., 1977, 622 pp. | MR

[3] P. S. Landa, Nelineinye volny, Mir, M., 1983, 320 pp. | MR

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

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

[6] S. D. Glyzin, A. Yu. Kolesov, “Ustanovivshiesya rezhimy uravneniya Khatchinsona s maloi diffuziei v sluchae kvadrata”, Kachestvennye metody issledovaniya operatornykh uravnenii, Yaroslavl, 1988, 44–54 | Zbl

[7] D. A. Kulikov, “Bifurkatsii ploskikh voln obobschennogo kubicheskogo uravneniya Shredingera v tsilindricheskoi oblasti”, Model. i analiz inform. sistem, 13:1 (2006), 20–26

[8] D. A. Kulikov, “Struktura okrestnosti beguschikh voln obobschennogo kubicheskogo uravneniya Shredingera v tsilindricheskoi oblasti”, Izvestiya RAEN. Differentsialnye uravneniya, 2006, no. 11, 135–137 | MR

[9] S. L. Sobolev, Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Izd-vo Leningradskogo gos. un-ta, L., 1950, 255 pp. | MR

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