Nonlinear edge modes from topological one-dimensional lattices

We propose a method to address the existence of topological edge modes in one-dimensional (1D) nonlinear lattices, by deforming the edge modes of linearized models into solutions of the fully nonlinear system. For sufficiently large nonlinearites, the energy of the modified edge modes may eventually shift out of the gap, leading to their disappearance. We identify a class of nonlinearities satisfying a generalized chiral symmetry where this mechanism is forbidden, and the nonlinear edge states are protected by a topological order parameter. Different behaviors of the edge modes are then found and explained by the interplay between the nature of the nonlinarities and the topology of the linearized models.