Supersonic solitary waves in non-local bistable lattices

Non-local interactions are receiving increasing attention in the control of wave propagation in metamaterials. Nevertheless, the role of non-local interactions in shaping solitary wave profiles, admissible supersonic regimes, stability, and instability-induced evolution remains largely unexplored. To address these challenges, supersonic solitary waves in bistable lattices are studied through a combined theoretical and numerical approach, revealing how non-local effects govern their wave dynamics. We first demonstrate that non-locality serves as an effective tool for tuning wave morphology: positive stiffness coupling leads to wave broadening, whereas negative stiffness coupling enhances localization. More importantly, we reveal that strong negative stiffness interactions fundamentally alter the dispersion relation, thereby redefining the supersonic regimes where supersonic solitary waves exist. Furthermore, it is found that weak negative stiffness non-locality can enhance the stability of solitary waves, standing in sharp contrast to other non-local interactions that tend to shrink the stable domain. When stability is lost, two distinct evolution pathways are identified: one involves a nonlinear self-adjustment toward a stable high-speed attractor, and the other entails a fission process that generates multiple coherent structures, including transmitted/reflected waves and pinned breathing waves. Finally, during boundary interactions, non-local effects are crucial both for maintaining wave integrity and for potentially mediating the conversion between solitary and transitional waves. These findings provide a robust theoretical foundation for designing advanced mechanical metamaterials with programmable wave characteristics.