Nonreciprocal nonlocal elastic topological soliton

This work presents the competing roles of nonreciprocal advection and elastic stiffness in governing topological soliton dynamics within a one-dimensional rotator chain. The lattice model incorporates three independently tunable mechanical couplings: nearest-neighbor stiffness, fixed-span nonlocal stiffness, and a spatially uniform antisymmetric (nonreciprocal) coupling that introduces nonconservative directional forcing. A continuum reduction is performed to extract the dominant advective and elastic contributions, yielding scaling relations for propagation speed and intrinsic soliton width. Numerical experiments, benchmarked against a baseline configuration, demonstrate a continuous transition from coherent translation, through radiation-dominated propagation, to localized oscillatory trapping as the effective elastic length scale increases relative to advective strength. The antisymmetric coupling provides linear control of drift velocity, consistent with an overdamped scaling analysis. The two elastic couplings collectively determine an effective stiffness that sets the soliton width; larger widths enhance spectral overlap with linear lattice modes, promoting radiative losses. These findings establish a parameter-phase diagram that delineates regimes suitable for three operational modalities: high-fidelity directional transport, programmable radiation, and local energy trapping. This work offers a systematic framework for designing programmable wave-control devices in nonreciprocal mechanical metamaterials.