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    The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg–Landau equation

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    Type
    Article
    Authors
    Aguareles, M.
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2014-06
    Permanent link to this record
    http://hdl.handle.net/10754/599899
    
    Metadata
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    Abstract
    In this paper we consider an oscillatory medium whose dynamics are modeled by the complex Ginzburg-Landau equation. In particular, we focus on n-armed spiral wave solutions of the complex Ginzburg-Landau equation in a disk of radius d with homogeneous Neumann boundary conditions. It is well-known that such solutions exist for small enough values of the twist parameter q and large enough values of d. We investigate the effect of boundaries on the rotational frequency of the spirals, which is an unknown of the problem uniquely determined by the parameters d and q. We show that there is a threshold in the parameter space where the effect of the boundary on the rotational frequency switches from being algebraic to exponentially weak. We use the method of matched asymptotic expansions to obtain explicit expressions for the asymptotic wavenumber as a function of the twist parameter and the domain size for small values of q. © 2014 Elsevier B.V. All rights reserved.
    Citation
    Aguareles M (2014) The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg–Landau equation. Physica D: Nonlinear Phenomena 278-279: 1–12. Available: http://dx.doi.org/10.1016/j.physd.2014.03.007.
    Sponsors
    The author thanks S.J. Chapman and T. Witelski for stimulating discussions. M. Aguareles has been supported in part by grants from the Spanish Government (MTM2011-27739-C04-03), from the Catalan Government (2009SGR345) and also by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). The author would also like to thank the center OCIAM of the University of Oxford where part of this research was carried out.
    Publisher
    Elsevier BV
    Journal
    Physica D: Nonlinear Phenomena
    DOI
    10.1016/j.physd.2014.03.007
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.physd.2014.03.007
    Scopus Count
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