2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79889We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized states, and also reveal an important physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.4 pages, 5 figuresPattern Formation and SolitonsCondensed MatterOpticstext