Geodesic
Stability of dark screening solitons in photorefractive media
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 49-58 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Biased photorefractive media are known to admit bright and dark solitons. The bright solitons in these media are always stable, but their dark counterparts are unstable above a certain background intensity and below a critical velocity. We use the stability criterion and the Vakhitov–Kolokolov function to precisely determine the unstable-parameter region. We also predict the strength of the instability by determining the unstable eigenvalues and eigenmodes using the Evans function method. Numerical simulation of the full evolution equation confirms the results.
Keywords: photorefractive medium, dark soliton, stability, Evans function. 
@article{TMF_2009_160_1_a4,
     author = {M. Facao and M. I. Carvalho},
     title = {Stability of dark screening solitons in photorefractive media},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {49--58},
     year = {2009},
     volume = {160},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a4/}
}
TY  - JOUR
AU  - M. Facao
AU  - M. I. Carvalho
TI  - Stability of dark screening solitons in photorefractive media
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2009
SP  - 49
EP  - 58
VL  - 160
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a4/
LA  - ru
ID  - TMF_2009_160_1_a4
ER  - 
%0 Journal Article
%A M. Facao
%A M. I. Carvalho
%T Stability of dark screening solitons in photorefractive media
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2009
%P 49-58
%V 160
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a4/
%G ru
%F TMF_2009_160_1_a4
M. Facao; M. I. Carvalho. Stability of dark screening solitons in photorefractive media. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 49-58. http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a4/

[1] D. N. Christodoulides, M. I. Carvalho, J. Opt. Soc. Amer. B, 12:9 (1995), 1628–1633 | DOI

[2] M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, P. di Porto, Electron. Lett., 31:10 (1995), 826–827 | DOI

[3] M. Shih, P. Leach, M. Segev, G. Salamo, M. H. Garret, G. C. Valley, Opt. Lett., 21:5 (1996), 324–326 | DOI

[4] G. C. Duree Jr., J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. di Porto, E. J. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett., 71:4 (1993), 533–536 | DOI

[5] M. Facão, D. F. Parker, Phys. Rev. E, 68:1 (2003), 016610 | DOI

[6] A. G. Grandpierre, D. N. Christodoulides, T. H. Coskun, M. Segev, Y. S. Kivshar, J. Opt. Soc. Amer. B, 18:1 (2001), 55–63 | DOI

[7] I. V. Barashenkov, Phys. Rev. Lett., 77:7 (1996), 1193–1197 | DOI

[8] Z. Lin, Adv. Differential Equations, 7:8 (2002), 897–918 | MR | Zbl

[9] L. Di Menza, C. Gallo, Nonlinearity, 20:2 (2007), 461–496 | DOI | MR | Zbl

[10] D. Khenri, Geometricheskaya teoriya polulineinykh parabolicheskikh uravnenii, Mir, M., 1985 | MR | MR | Zbl

[11] J. Alexander, R. Gardner, C. Jones, J. Reine Angew. Math., 410 (1990), 167–212 | MR | Zbl

[12] D. E. Pelinovsky, P. G. Kevrekidis, Z. Angew. Math. Phys., 59:4 (2008), 559–599 | DOI | MR | Zbl

[13] N. G. Vakhitov, A. A. Kolokolov, Izv. vuzov. Ser. radiofizika, 16:7 (1973), 1020–1028 | DOI