Wave Packet Dynamics in Uniform Chain with Various Spatial Distributions of Nonlinearity

Abstract

We considered the dynamical properties of an initially localized wave packet in one-dimensional uniform lattices with various spatial distributions of nonlinearity. For the spatial uniform distribution of nonlinearity, solitons appear and move in opposite directions away from the initial site by weak nonlinearity. For moderate nonlinearity, the wave packet is totally diffusive. For strong nonlinearity, self trapping phenomenon occurs. For the spatial periodic and disordered distributions of nonlinearity, the wave packet is totally diffusive for weak and moderate nonlinearity. When the nonlinearity is strong, self trapping appears. For the spatial quasiperiodic Fibonacci distribution of nonlinearity, the wave packet is totally diffusive for weak nonlinearity. For moderate nonlinearity, the moving solitons appear. Self trapping appears for strong nonlinearity. We hope that our results can be useful in motivating and guiding experiments on the expansion of cold atoms in uniform optical lattices.