Chaos control in the nonlinear Schrödinger equation with Kerr law nonlinearity

doi:10.1088/1674-1056/23/2/020204

Abstract The nonlinear Schrödinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.

Keywords: chaos control fiber-optic signal nonlinear Schrödinger equation

Received: 24 April 2013
Revised: 19 July 2013
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11101191).

Corresponding Authors: Yin Jiu-Li
E-mail: yjlujs@yahoo.com.cn

About author: 02.30.Jr; 02.60.Lj

Cite this article:

Yin Jiu-Li (殷久利), Zhao Liu-Wei (赵刘威), Tian Li-Xin (田立新) Chaos control in the nonlinear Schrödinger equation with Kerr law nonlinearity 2014 Chin. Phys. B 23 020204

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