Robustness analysis of externally driven damped solitons in the presence of uncertainties and disorders

Abstract

This paper investigates the sensitivity of localized vibrations phenomena in externally driven Duffing oscillator chains. Such investigation is conducted by generalizing the Nonlinear Schrödinger Equation (NLSE) to accommodate disorder functions in all physical parameters, beyond impurities commonly found in the literature, limited to the natural frequency of the components. Given the absence of closed-form solutions for externally driven damped systems, we employ a numerical method, followed by statistical analysis, to elucidate the effects of parameter uncertainties across the lattice on solitons behavior. Our findings highlight the diverse effects of the physical nature of uncertainties within the mechanical structure, offering insights into possible experimental investigations. Additionally, we illustrate how specific impurities along the chain, capable to nucleate oscillations, mitigate resonant chaotic behaviors, reinforcing soliton stability. The results affirm the feasibility of generating standing waves in nonlinear lattices, emphasizing their relevance beyond traditional periodic assumptions, where uncertainties in physical parameters are commonly disregarded.