## ABSTRACT

In solid-state physics, the phenomenon of localization is usually perceived as arising from extrinsic disorder that breaks the discrete translational invariance of the perfect crystal lattice. Familiar examples include the localized vibrational modes around impurities or defects in crystals and Anderson localization of waves in disordered media [1]. The usual perception among solid-state researchers is that, in perfect lattices excitations must be extended objects as well, essentially plane wave like. Such firmly entrenched perceptions were severely jolted since the discovery of discrete breathers (DBs), also known as intrinsic localized modes (ILM). These states are typical excitations in perfectly periodic but strongly nonlinear systems, and are characterized by being spatially localized, at variance to plane wave states [2-4].