Chaos appears in the whole process of fiber-optic signal propagation with
one external perturbation due to the absence of damping. Via adding a proper controller,
chaos cannot be suppressed when the controller’s strength is weak. With the increase
of the controller strength, the fiber-optic signal can stay in a stable state. However,
unstable phenomenon occurs in the propagation of the fiber-optic signal when
the strength exceeds a certain degree. Moreover, we discuss the parameters’
sensitivity to be controlled. Numerical results show that vibration, oscillation
and escape can occur during the transmission of optic signals with different
parametric regions.
Cite this paper
Xing, Q. , Yin, J. and Tian, L. (2014). Analysis on the Propagation of the Fiber-Optic Signals in the Perturbed Nonlinear Schrodinger Equation. Open Access Library Journal, 1, e721. doi: http://dx.doi.org/10.4236/oalib.1100721.
de Bouard, A. and Debussche, A. (2010) The Nonlinear Schrodinger Equation with
White Noise Dispersion. Journal of
Functional Analysis, 259, 1300-1321. http://dx.doi.org/10.1016/j.jfa.2010.04.002
Nakkeeran, K. and
Wai, P.K.A. (2005) Generalized Projection Operator
Method to Derive the Pulse Parameters Equations for the Nonlinear Schrodinger Equation. Optics Communications, 244, 377-382. http://dx.doi.org/10.1016/j.optcom.2004.09.022
Ndzana, F., Mohamadou, A. and Kofané, T.C. (2007) Modulational Instability in the Cubic-Quintic
Nonlinear Schrodinger Equation through the Variational Approach. Optics Communications, 275, 421-428. http://dx.doi.org/10.1016/j.optcom.2007.02.036
Hoseini, S.M. and Marchant, T.R.
(2010) Evolution of Solitary Waves for a Perturbed Nonlinear Schrodinger Equation. Applied Mathematics and Computation, 216,
3642-3651. http://dx.doi.org/10.1016/j.amc.2010.05.015
Dereli, Y., Irk,
D. and Dag, I. (2009) Chaos, Soliton Solutions for NLS Equation Using Radial Basis Functions. Solitons and Fractals, 42, 1227-1233. http://dx.doi.org/10.1016/j.chaos.2009.03.030
Shlizerman, E. and
Rom-Kedar, V. (2006) Three Types of Chaos in the Forced Nonlinear
Schrodinger Equation. Physical Review
Letters, 96, Article ID: 024104. http://dx.doi.org/10.1103/PhysRevLett.96.024104
Korabel, N. and Zaslavsky, G.M. (2007) Transition to Chaos in Discrete Nonlinear
Schrodinger Equation with Long- Range Interaction. Physica A, 378, 223-237. http://dx.doi.org/10.1016/j.physa.2006.10.041
Sharma, A., Patidar,
V., Purohit, G., Sud,
K.K. and Bishop, A.R.
(2012) Effects on the Bifurcation and Chaos in Forced Duffing Oscillator Due to
Nonlinear Damping. Communications in
Nonlinear Science and Numerical Simulation, 17, 2254-2269. http://dx.doi.org/10.1016/j.cnsns.2011.10.032
Jing, Z.J., Huang,
J.C. and Deng, J. (2007) Complex Dynamics in Three-Well Duffing System with Two External Forcings. Chaos, Solitions & Fractals, 33, 795-812. http://dx.doi.org/10.1016/j.chaos.2006.03.071
Li, P., Yang,
Y.R. and Zhang, M.L. (2011) Melnikov’s Method for Chaos of a Two-Dimensional Thin
Panel in Subsonic Flow with External Excitation. Mechanics
Research Communications, 38, 524-528. http://dx.doi.org/10.1016/j.mechrescom.2011.07.008