Soliton solutions and self-steepening in the photon-conserving nonlinear Schrödinger equation

Hernández, S. M.; Bonetti, J.; Linale, N.; Grosz, D. F.; Fierens, Pablo Ignacio

doi:10.1080/17455030.2020.1856970

Cited by 11 publications

(1 citation statement)

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“…This equation is capable of describing a variety of nonlinear phenomena beyond mechanical context. Recent examples have reported the use of NLSE in biology [18] and photonics [19], for example. From this perspective, the search for solutions of NLSE is of special interest not only for mechanical engineering but also for the study of nonlinear phenomena in general.…”

Section: Introductionmentioning

confidence: 99%

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

Barbosa

Kacem

Bouhaddi

2023

Preprint

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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.

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Section: Introductionmentioning

confidence: 99%