Melnikov's criteria and chaos analysis in the nonlinear Schrödinger equation with Kerr law nonlinearity
type: Item
instance of: scholarly article
title: Melnikov's criteria and chaos analysis in the nonlinear Schrödinger equation with Kerr law nonlinearity
zbMATH Open document ID: 1474.35591
DOI: 10.1155/2014/650781
author: Jiuli Yin
author: Liuwei Zhao
author: Lixin Tian
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: The dynamics of the nonlinear Schrödinger equation with Kerr law nonlinearity with two perturbation terms are investigated. By using Melnikov method, the threshold values of chaotic motion under periodic perturbation are given. Moreover we also study the effects of the parameters of system on dynamical behaviors by using numerical simulation. The numerical simulations, including bifurcation diagram of fixed points, chaos threshold diagram of system in three-dimensional space, maximum Lyapunov exponent, and phase portraits, are also plotted to illustrate theoretical analysis and to expose the complex dynamical behaviors. In particular, we observe that the system can leave chaotic region to periodic motion by adjusting controller \(e\), amplitude \(d_1\), and frequency \(\omega_2\) of external forcing which can be considered a control strategy, and when the frequenciesy \(\omega_2\) and \(\omega_1\) approach the maximum frequency of disturbance, the system turmoil intensifies and control intensity increases.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 7022829
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/650781
OpenAlex ID: W1988343183
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Wikidata QID: Q59040373
description: scientific article; zbMATH DE number 7022829