Coherent Structures Generated by Inhomogeneities in Oscillatory Media | Zendy

Richard Kollár | Zendy; Arnd Scheel | Zendy

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Coherent Structures Generated by Inhomogeneities in Oscillatory Media

Author(s) -

Richard Kollár,

Arnd Scheel

Publication year - 2007

Publication title -

siam journal on applied dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.218

H-Index - 61

ISSN - 1536-0040

DOI - 10.1137/060666950

Subject(s) - physics , homogeneous , wavenumber , oscillation (cell signaling) , modulation (music) , phase space , dimension (graph theory) , diffusion , space (punctuation) , reaction–diffusion system , traveling wave , classical mechanics , statistical physics , mathematical analysis , optics , quantum mechanics , mathematics , philosophy , genetics , acoustics , pure mathematics , biology , linguistics

We investigate the effect of spatially localized inhomogeneities on a spatially homo- geneous oscillation in a reaction-diffusion system. In dimension up to 2, we find sources and contact defects, that is, the inhomogeneity may either send out phase waves or act as a weak sink. We show that small inhomogeneities cannot act as sources in more than 2 space dimensions. We also derive asymptotics for wavenumbers and group velocities in the far field. The results are established rigorously for radially symmetric inhomogeneities in reaction-diffusion systems, and for arbitrary inhomogeneities in a modulation equation approximation.

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