Abstract
Regular one-dimensional patterns in systems with a reflection symmetry and a conserved quantity may be unstable to an instability leading to strong spatial modulation of the pattern. For certain parameter valuesallregular patterns may be unstable at onset; simulations then indicate the existence of stable strongly modulated patterns. Analysis of the instability has hitherto assumed that the linear growth rate of disturbances isO(k 2)as the wavenumberk → 0. However, the instability is shown here to be present even when there is slight damping of the modes withk → 0, corresponding to a slight breaking of the conservation law.
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© 2003 Springer Basel AG
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Cox, S.M., Matthews, P.C. (2003). One-dimensional Pattern Formation in Systems with a Conserved Quantity. In: Buescu, J., Castro, S.B.S.D., da Silva Dias, A.P., Labouriau, I.S. (eds) Bifurcation, Symmetry and Patterns. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7982-8_10
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DOI: https://doi.org/10.1007/978-3-0348-7982-8_10
Publisher Name: Birkhäuser, Basel
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