Geodesic
Analysis of running waves stability in the Ginzburg–Landau equation with small diffusion
Modelirovanie i analiz informacionnyh sistem, Tome 18 (2011) no. 3, pp. 58-62 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the local dynamics of the Ginzburg–Landau equation with small diffusion in a neibourhood of running waves. We find necessary conditions of running waves instability and sufficient conditions of their stability.
Keywords: running wave, small parameter, Ginzburg–Landau equation. 
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     title = {Analysis of running waves stability in the {Ginzburg{\textendash}Landau} equation with small diffusion},
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A. A. Kashchenko. Analysis of running waves stability in the Ginzburg–Landau equation with small diffusion. Modelirovanie i analiz informacionnyh sistem, Tome 18 (2011) no. 3, pp. 58-62. http://geodesic.mathdoc.fr/item/MAIS_2011_18_3_a5/

[1] V. I. Ginzburg, L. D. Landau, “K teorii sverkhprovodimosti”, ZhETF, 20 (1950), 1064

[2] N. A. Kudryashov, Metody nelineinoi matematicheskoi fiziki, Uchebnoe posobie, Intellekt, Dolgoprudnyi, 2010, 368 pp.

[3] T. S. Akhromeeva, S. P. Kurdyumov, G. G. Malinetskii, A. A. Samarskii, Nestatsionarnye struktury i diffuzionnyi khaos, Nauka, M., 1992, 542 pp. | MR | Zbl