Localized and periodic exact solutions to the nonlinear Schrodinger   equation with spatially modulated parameters: Linear and nonlinear lattices
  Using similarity transformations we construct explicit solutions of the nonlinear Schrodinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their properties. We put our results in the framework of the exploited perturbation techniques and discuss their implications on the properties of associated linear periodic potentials and on the possibilities of stabilization of gap solitons using polychromatic lattices. 
Juan Belmonte Beitia, Vladimir V. Konotop, Victor M. Perez Garcia and   Vadym E. Vekslerchik