Standing Solitons Tuned by Impurities in Damped Nonlinear Lattices under External Excitation

Abstract

Periodic chains of nonlinear oscillators are known to support solitonic solutions within a specific range of physical parameters when damping effect is considered. This Letter investigates the dynamics of stationary solitons in damped nonlinear lattices under external excitation, focusing on the influence of impurities related to the natural frequency of the oscillators. We demonstrate experimentally and numerically that incorporating impurities into externally driven periodic lattices can expand the solitonic stability diagram under high-damping areas and near the Hopf bifurcation of periodic structures. A mathematical description that closely aligns with experimental realities is presented through the disordered damped nonlinear Schrödinger equation. Specifically, we prove how impurities along the chain can spontaneously nucleate the lattice solitons. The obtained results open the way toward the functionalization of disorder to control nonlinear energy localization in damped nonperiodic structures.