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Type: Journal article
Title: Oscillatory pattern formation with a conserved quantity
Author: Winterbottom, D. M.
Matthews, P. C.
Cox, Stephen Michael
Citation: Nonlinearity, 2005; 18(3):1031-1056
Publisher: IOP Publishing Ltd
Issue Date: 2005
ISSN: 0951-7715
School/Discipline: School of Mathematical Sciences
Statement of
D M Winterbottom, P C Matthews and S M Cox
Abstract: The influence of a conserved quantity on an oscillatory pattern-forming instability is examined in one space dimension. Amplitude equations are derived which are not only generic for systems with a pseudoscalar conserved quantity (e.g. rotating convection, magnetoconvection) but also applicable to systems with a scalar conserved quantity. The stability properties of both travelling and standing waves are analysed, with particular progress being possible in the limit of long-wavelength perturbations. For both forms of waves, the corresponding modulational stability boundaries are significantly altered by the presence of the conserved quantity; also, new instabilities are generated. For general perturbations, the full stability regions are found numerically. Simulations of the nonlinear governing equations are performed using a pseudo-spectral code; a variety of stable attractors are thus found of varying degrees of complexity. Previously unseen, highly localized, solutions are observed.
DOI: 10.1088/0951-7715/18/3/006
Appears in Collections:Mathematical Sciences publications

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