Nonlinearity effect on 1D periodic and disordered lattices

The Kronig-Penney model is used to Study the effect of nonlinear interaction on the transmissive properties of both ordered and disordered chains. In the ordered case, the nonlinearity can either localize or delocalize the electronic states depending on both its sign and strength but there is a critical strength above which all the states are localized. In the disordered case, however, we found that the transmission decays as $T\sim L^{-\gamma}$ around the band edge of the corresponding periodic system. The exponent $\gamma$ is independent of the strength of the nonlinearity in the case of disordered barrier potentials, while it varies with the strength for mixed potentials.