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Analysis of running waves stability in the Ginzburg–Landau equation with small diffusion

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Abstract

The local dynamics of the Ginzburg–Landau equation with small diffusion and periodic boundary conditions in the neighborhood of running waves is analyzed. Sufficient conditions for the instability of running waves and sufficient conditions for their stability are found.

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References

  1. Ginzburg, V.I. and Landau, L.D., On the theory of superconductivity, Zh. Eksp. Teor. Fiz., 1950, vol. 20, p. 1064.

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Authors and Affiliations

  1. Demidov Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia

    A. A. Kashchenko

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  1. A. A. Kashchenko
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Correspondence to A. A. Kashchenko.

Additional information

Original Russian Text © A.A. Kashchenko, 2011, published in Modelirovanie i Analiz Informatsionnykh Sistem, 2011, No. 3, pp. 58–62.

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Kashchenko, A.A. Analysis of running waves stability in the Ginzburg–Landau equation with small diffusion. Aut. Control Comp. Sci. 49, 514–517 (2015). https://doi.org/10.3103/S0146411615070093

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  • DOI: https://doi.org/10.3103/S0146411615070093

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