Localized states in bistable pattern-forming systems.
We present a unifying description close to a spatial bifurcation of localized states, appearing as large amplitude peaks nucleating over a pattern of lower amplitude. Localized states are pinned over a lattice spontaneously generated by the system itself. We show that the phenomenon is generic and requires only the coexistence of two spatially periodic states. At the onset of the spatial bifurcation, a forced amplitude equation is derived for the critical modes, which accounts for the appearance of localized peaks.
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Institut Non Linéaire de Nice, UMR 6618, 1361 Route des Lucioles, 06560 Valbonne, France.
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