Breatherlike impurity modes in discrete nonlinear lattices

We investigate the properties of a disordered generalized discrete nonlinear Schrödinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant breather states in the vicinity of the impurities. We analyze the properties of these breathers analytically and numerically.