Nonlinear dynamics of a generalized higher-order nonlinear Schrödinger equation with a periodic external perturbation

The nonlinear dynamics of a generalized higher-order nonlinear Schrödinger (HNLS) equation with a periodic external perturbation is investigated numerically. Via the phase plane analysis, we find that both the homoclinic orbits and heteroclinic orbits can exist for the unperturbed HNLS equation unde...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear dynamics 2016-10, Vol.86 (1), p.535-541
Main Authors: Li, Min, Wang, Lei, Qi, Feng-Hua
Format: Article
Language:English
Subjects:
Automotive Engineering
Bifurcations
Chaos theory
Classical Mechanics
Control
Control methods
Dynamical Systems
Engineering
Evolution
Feedback control
Mathematical analysis
Mechanical Engineering
Nonlinear dynamics
Nonlinear systems
Orbits
Original Paper
Perturbation
Perturbation methods
Schrodinger equation
Schroedinger equation
Solitary waves
Vibration
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The nonlinear dynamics of a generalized higher-order nonlinear Schrödinger (HNLS) equation with a periodic external perturbation is investigated numerically. Via the phase plane analysis, we find that both the homoclinic orbits and heteroclinic orbits can exist for the unperturbed HNLS equation under certain conditions, which respectively corresponds to the bell-shaped and kink-shaped soliton solutions. Moreover, under the effect of the periodic external perturbation, the quasi-periodic bifurcations arise and can evolve into the chaos. The dynamical responses of the perturbed system varying with the perturbation strength and two types of chaotic attractors are discussed to show the existence of the chaotic motions. Via the feedback control methods, such chaotic motions are found to be controlled effectively and finally evolve into the stable quasi-periodic orbits. All the results are helpful to understand the dynamical properties of the nonlinear system.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-016-2906-y