A design methodology for nonlinear oscillator chains enabling energy localization tuning and soliton stability enhancement with optimal damping

Abstract

In this paper, Intrinsic Localized Modes (ILMs) are investigated in coupled nonlinear oscillators, with a specific focus on creating stationary solitons. The main objective is to establish a design methodology for reproducing the Nonlinear Schr¨odinger Equation (NLSE) in mechanical systems, even in the presence of damping. A three-dimensional diagram is developed in order to illustrate stable parameter regions for damped stationary solitons. Moreover an analysis of the influence of the number of oscillators in the system, and a numerical investigation regarding the stability of solitonic behavior is done. Through numerical analyses, it is observed that the developed algorithm not only has the capability to locate the highest amplitudes in the chain of oscillators but also to control the intensity at which these amplitudes are located according to design requirements. The proposed methodology expands the understanding of energy localization in nonlinear systems and holds potential for practical applications.