  Quantum transport in a class of nonlinear extensions of the Rudner-Levitov
model is numerically studied in this paper. We show that the quantization of
the mean displacement, which embodies the quantum coherence and the topological
characteristics of the model, is markedly modified by nonlinearities. Peculiar
effects such as a "trivial-nontrivial" transition and unidirectional long-range
quantum transport are observed. These phenomena can be understood on the basis
of the dynamic behavior of the effective hopping terms, which are time and
position dependent, containing contributions of both the linear and nonlinear
couplings.d nonlinear couplings.
