Analysis on the Propagation of the Fiber-Optic Signals in the Perturbed Nonlinear Schrödinger Equation

DOI: 10.4236/oalib.1100721   PDF        1,117 Downloads   1,344 Views  


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.

Share and Cite:

Xing, Q. , Yin, J. and Tian, L. (2014) Analysis on the Propagation of the Fiber-Optic Signals in the Perturbed Nonlinear Schrödinger Equation. Open Access Library Journal, 1, 1-11. doi: 10.4236/oalib.1100721.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] de Bouard, A. and Debussche, A. (2010) The Nonlinear Schrödinger Equation with White Noise Dispersion. Journal of Functional Analysis, 259, 1300-1321.
[2] Nakkeeran, K. and Wai, P.K.A. (2005) Generalized Projection Operator Method to Derive the Pulse Parameters Equations for the Nonlinear Schrödinger Equation. Optics Communications, 244, 377-382.
[3] Ndzana, F., Mohamadou, A. and Kofané, T.C. (2007) Modulational Instability in the Cubic-Quintic Nonlinear Schrödinger Equation through the Variational Approach. Optics Communications, 275, 421-428.
[4] Hoseini, S.M. and Marchant, T.R. (2010) Evolution of Solitary Waves for a Perturbed Nonlinear Schrödinger Equation. Applied Mathematics and Computation, 216, 3642-3651.
[5] Dereli, Y., Irk, D. and Dag, I. (2009) Chaos, Soliton Solutions for NLS Equation Using Radial Basis Functions. Solitons and Fractals, 42, 1227-1233.
[6] Korabel, N. and Aslavsky, G.M.Z. (2007) Transition to Chaos in Discrete Nonlinear Schrödinger Equation. Physica A, 378, 223-237.
[7] Shlizerman, E. and Rom-Kedar, V. (2006) Three Types of Chaos in the Forced Nonlinear Schrödinger Equation. Physical Review Letters, 96, Article ID: 024104.
[8] Kivshar, Y.S. and Pelinovsky, D.E. (2000) Self-Focusing and Transverse Instabilities of Solitary Waves. Physics Reports, 331, 117-195.
[9] Korabel, N. and Zaslavsky, G.M. (2007) Transition to Chaos in Discrete Nonlinear Schrödinger Equation with Long-Range Interaction. Physica A, 378, 223-237.
[10] Henning, D. and Tsironis, G.P. (1999) Wave Transmission in Nonlinear Lattices. Physics Reports, 307, 333-432.
[11] 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.
[12] 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.
[13] Wang, R.Q., Deng, J. and Jing, Z.J. (2006) Chaos Control in Duffing System. Chaos, Solitons and Fractals, 27, 249-257.
[14] Stanton, S.C., Mann, B.P. and Owens, B.A.M. (2012) Melnikov Theoretic Methods for Characterizing the Dynamics the Bistable Piezoelectric Inertial Generator in Complex Spectral Environments. Physica D, 241, 711-720.
[15] 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.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.