Localized states in bi-pattern systems

M. G. Clerc, U. Bortolozzo, F. Haudin, R. G. Rojas, S. Residori

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We present a unifying description of localized states observed in systems with coexistence of two spatially periodic states, called bi-pattern systems. Localized states are pinned over an underlying lattice that is either a self-organized pattern spontaneously generated by the system itself, or a periodic grid created by a spatial forcing. We show that localized states are generic and require only the coexistence of two spatially periodic states. Experimentally, these states have been observed in a nonlinear optical system. At the onset of the spatial bifurcation, a forced one-dimensional amplitude equation is derived for the critical modes, which accounts for the appearance of localized states. By numerical simulations, we show that localized structures persist on two-dimensional systems and exhibit different shapes depending on the symmetry of the supporting patterns.

Original languageEnglish
Article number926810
JournalAdvances in Nonlinear Optics
StatePublished - 2009
Externally publishedYes


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