Abstract
Spatially extended systems with nonlocal dynamics (e.g. ferromagnetic resonance or current instability) of the type ∂tu = fμ;1L∫0Ludx, u, ∂2xu, ∂4xu,… with uϵRn will be studied near the soft-mode instability (wave number kc ≠ 0) of a stationary and uniform state. An amplitude equation is derived within the framework of a multiple-scale perturbation theory. A particular example of this class of nonlocal dynamics is also treated numerically. As the main result we find that in contrast to the well-known supercritical bifurcation into a stable periodic state, the uniform state can bifurcate supercritically into a stationary state of an amplitude-modulated fast oscillation in space.
Published Version
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