Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/17749
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dc.contributor.authorWinterbottom, D. M.en
dc.contributor.authorMatthews, P. C.en
dc.contributor.authorCox, Stephen Michaelen
dc.date.issued2005en
dc.identifier.citationNonlinearity, 2005; 18(3):1031-1056en
dc.identifier.issn0951-7715en
dc.identifier.urihttp://hdl.handle.net/2440/17749-
dc.description.abstractThe 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.en
dc.description.statementofresponsibilityD M Winterbottom, P C Matthews and S M Coxen
dc.language.isoenen
dc.publisherIOP Publishing Ltden
dc.titleOscillatory pattern formation with a conserved quantityen
dc.typeJournal articleen
dc.contributor.schoolSchool of Mathematical Sciencesen
dc.identifier.doi10.1088/0951-7715/18/3/006en
Appears in Collections:Mathematical Sciences publications

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