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Fourier-Bessel analysis of patterns in a circular domain. (English) Zbl 1076.35535
Summary: This paper explores the use of the Fourier-Bessel analysis for characterizing patterns in a circular domain. A set of stable patterns is found to be well-characterized by the Fourier-Bessel functions. Most patterns are dominated by the principal Fourier-Bessel mode \([n,m]\) which has the largest Fourier-Bessel decomposition amplitude when the control parameter \(R\) is close to the corresponding nontrivial root \((\rho_{n,m})\) of the Bessel function. Moreover, when the control parameter is chosen to be close to two or more roots of the Bessel function, the corresponding principal Fourier-Bessel modes compete to dominate the morphology of the patterns.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
33C90 Applications of hypergeometric functions
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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