D M Winterbottom et al 2005 Nonlinearity 18 1031 doi:10.1088/0951-7715/18/3/006
Oscillatory pattern formation with a conserved quantity
D M Winterbottom1, P C Matthews1 and S M Cox2
Show affiliationsRecommended by J Lega
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.
- PACS
- MSC
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37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion
- Subjects
- Dates
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Issue 3 (May 2005)
Received 3 June 2004, in final form 13 December 2004
Published 9 February 2005
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Oscillatory pattern formation with a conserved quantity
D M Winterbottom et al 2005 Nonlinearity 18 1031
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