Nonlinear energy transmission in systems with nonlocal effects and relativistic potentials

Abstract

In this work, we consider bounded one-dimensional systems consisting of particles with relativistic potentials and nonlocal interactions. The systems are initially at rest and at equilibrium, and are perturbed sinusoidally at one end. Meanwhile, we consider an absorbing boundary at the other end. A Hamiltonian computational method is employed in this work to simulate the dynamics of the continuous-time system. We show here that the driving boundary propagates energy into the system in the form of nonlinear modes. For each driving frequency at the forbidden band-gap, this process occurs at a critical amplitude: the supratransmission threshold. We find that supratransmission occurs for all frequencies in the forbidden band-gap independently of whether nearest-neighbor or global interactions are considered. Several qualitative conclusions are obtained in this work based on our computational results.