Localized and periodic exact solutions to the nonlinear Schr_dingerequation with spatially modulated parameters: Linear and nonlinearlattices

摘要

Using similarity transformations we construct explicit solutions of the nonlinear Schr_-dinger equation with linear and nonlinear periodic potentials. We present explicit formsof spatially localized and periodic solutions, and study their properties. We put our resultsin the framework of the exploited perturbation techniques and discuss their implicationson the properties of associated linear periodic potentials and on the possibilities of stabil-ization of gap solitons using polychromatic lattices.