The effect of the rectangular and sawtooth piecewise onsite terms on the wave transmission in the one-dimensional discrete nonlinear Schrödinger lattices

Abstract

In this work, we studied a one-dimensional discrete Schrodinger equation in the presence of rectangular and sawtooth potentials and nonlinearity. We created this discrete equation by using the numerical discretization of the continuous Schrodinger equation. We then calculated the transmission and reflection coefficients using some recursion relations. The effect of different parameters such as number of sites in the system, potential height, nonlinearity magnitude on the wave propagation is considered. Here, we addressed the creation and destruction of the band gaps and passbands and their position along the energy axis when these parameters changes.