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Prog. Theor. Phys. Vol. 71 No. 6 (1984) pp. 1182-1196

[ Full Text PDF : FREE ACCESS (906K) ]

Phase Dynamics of Weakly Unstable Periodic Structures

Yoshiki Kuramoto

Research Institute for Fundamental Physics, Kyoto University, Kyoto 606

(Received January 11, 1984)

Abstract:

Nonlinear phase dynamics of weakly unstable two-dimensional periodic patterns is studied. Four distinct physical situations are specifically considered. They correspond to the Eckhaus instability and zig-zag instability occurring in each of propagating and non-propagating patterns. Consequently, four prototype partial differential equations for phase function are obtained. Their derivation is totally based on symmetry- and scaling arguments. A simple interpretation of the origin of nonlinearity is given. Although the main part of the present theory is phenomenological, a more rigorous asymptonic theory is also developed for reaction-diffusion eqations.


URL : http://ptp.ipap.jp/link?PTP/71/1182/
DOI : 10.1143/PTP.71.1182

[ Full Text PDF : FREE ACCESS (906K) ] Citation:

References:

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