Insensitive non-reciprocal edge breathers

We uncover subtle and previously unexplored phenomena arising from the interplay of nonlinearity and non-reciprocity in topological mechanical metamaterials. We study a non-reciprocal topological Klein–Gordon chain of asymmetrically coupled nonlinear oscillators, which serves as a minimal mass–spring model capturing the features of several active nonreciprocal metamaterials across mechanical, electronic and acoustic platforms. We demonstrate that continuous families of non-reciprocal edge breathers (NEBs), namely boundary-localized, time-periodic waves, emerge from the linear edge mode as its amplitude increases. Remarkably, despite the absence of chiral or sublattice symmetries, we identify insensitive NEBs whose nonlinear frequency remains fixed to that of the linear edge mode with increasing nonlinearity. Our analysis reveals that the mechanism underlying this insensitivity stems from a competition between mode non-orthogonality and nonlinear interactions, yielding an exponential decay of the NEB nonlinear frequency shift with system size. Crucially, these insensitive NEBs also persist in the strongly nonlinear regime. Our work establishes a novel pathway towards realizing robust nonlinear topological waves in mechanical metamaterials without relying on symmetry-protected nonlinearities.