Nonlinear localized waves in a periodic medium
  We 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. 
Andrey A. Sukhorukov and Yuri S. Kivshar