Structural properties of self-localized steady-state modes in damped parametrically driven lattices have been numerically observed. The states are kinks, which are localized regions between two standing wave domains of the same wave number with an offset in spatial phase; and domain walls, which are localized regions between two standing wave domains of different wave numbers. The properties include preferred definite symmetry, a wide variety of distinct states, and hysteretic transitions that occur along boundaries in the plane of the drive parameters (amplitude and frequency). The transitions of the localized states exhibit the spontaneous processes of symmetry reversal and "complexification," as well as the onset of quasiperiodicity and chaos. Simple plausible models based upon few degrees of freedom fail to correctly describe the instabilities, which indicates that the behavior is a collective phenomenon.
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