Topological edge breathers in a nonlinear Su-Schrieffer-Heeger lattice

We show the existence of breathing edge modes in the Su-Schrieffer-Heeger model with cubic (Kerr) on-site nonlinearity, bifurcating from stationary edge solitons with propagation constant inside the topological gap of the linear model. These edge breathers are exact solutions to the nonlinear equations of motion, with time-periodic intensity oscillations and tails exponentially decaying from the edge. They bifurcate from two localized internal eigenmodes of the stationary edge soliton, having eigenfrequencies inside the topological gap and all higher harmonics above the linear spectrum. Numerical Floquet analysis for solutions obtained from a Newton scheme shows that edge breathers may be linearly stable even in regimes of large-amplitude oscillations, mainly manifested as time-periodic power exchange between the edge site and its next-nearest neighbor. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).