Abstract
We investigate the stability of spatially periodic states of the one-dimensional Newell-Whitehead-Segel amplitude equation extended by a spatially nonlocal term. The nonlocality is a convolution over the squared amplitude. We study the cross-over between local and strongly nonlocal behaviour by varying the width of the kernel between zero and infinity. We found a secondary instability, where spatially periodic states bifurcate supercritically into amplitude-modulated states with a modulation wavelength which scales with the width of the kernel.
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