Constant force amplifies pulse solitons via polarization coupling in mechanical metamaterials

Abstract

Unlike kink solitons with nonzero topological charge, pulse solitons cannot be driven by the experimentally most easily implemented constant force because of their zero topological charge. Here, we focus on a vector soliton with two polarization components: a pulse soliton component (rotation) and a kink soliton component (translation). We apply a constant force at the mass centers of the units, thereby driving the translational component with a constant force. Numerical simulations show that energy injected into the translational component can be transferred simultaneously to the rotational component through coupling, thereby achieving equal amplification of positive and negative pulses. Next, we change the application of this constant force to eccentric loading and find that the initially symmetric amplification of positive and negative solitons gradually becomes asymmetric over time. These phenomena are all explained by a theoretical model based on the adiabatic approximation, which gives a quantitative relation for the amplitude evolution, while the higher-order correction terms arising from the coupling effect also explain the origin of asymmetric transmission under eccentric driving. Our results demonstrate that vector solitons possess a unique capability for pulse soliton amplification by a constant force through polarization coupling and that this coupling can further modulate the symmetry between positive and negative pulses.