Abstract
This paper proposes an optical secure communication scheme based on chaos synchronization. Nonlinear Schrödinger equation is an important model for optical communication. Our theoretical analysis and numerical simulation show that when the nonlinear Schrödinger equation is perturbed by multiple frequencies, the optical solitons becomes chaotic despite that optical soliton is usual preferred for long-distance transmission. By taking the generated chaotic signals as communication carrier, a master slave system for optical secure communication is designed. A feedback controller is applied to the slave system. Sufficient conditions for chaos synchronization are then proved. It is discovered that the synchronization speed is closely linked with parameters of the nonlinear Schrödinger equation.
Similar content being viewed by others
References
Ahn, C.K.: A new chaos synchronization method for Duffing oscillator. IEICE Electr. Expr. 6, 1355–1360 (2009)
Chen, Y., Yan, Z.Y.: Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-hermitian PT-symmetric potentials. Sci. Rep. 6, 23478 (2016). doi:10.1038/srep23478
Hederi, M., Islas, A.L., Reger, K., Schober, C.M.: Efficiency of exponential time differencing schemes for nonlinear Schrödinger equations. Math. Comput. Simul. 127, 101–113 (2016)
Mahmoud, G.M., Mahmoud, E.E., Farghaly, A.A., Aly, S.A.: Chaotic synchronization of two complex nonlinear oscillators. Chaos Solitons Fractals 42, 2858–2864 (2009)
Mathieu, C., Masahito, O.: Instability of ground states for a quaslinear Schrödinger equation. Differ. Integral Equ. 27, 613–624 (2014)
Nottale, L.: Generalized quantum potentials. J. Phys. A Math. Theor. 42, 275306 (2009)
Sun, Y.J.: A novel chaos synchronization of uncertain mechanical systems with parameter mismatchings, external excitations, and chaotic vibrations. Commun. Nonlinear Sci. Numer. Simul. 17, 496–504 (2012)
Wang, B.X., Guan, Z.H.: Chaos synchronization in general complex dynamical networks withcoupling delays. Nonlinear Anal. Real World Appl. 11, 1925–1932 (2010)
Wang, X.L., Yang, J.: Exact spatiotemporal soliton solutions to the generalize three-dimensional nonlinear Schrödinger equation in optical fiber communication. Adv. Differ. Equ. 2015, 347 (2015)
Wang, S.B., Wang, X.Y., Zhou, Y.: A memristor-based complex Lorenz system and its modified projective synchronization. Entropy 17, 7628–7644 (2015)
Wembe, E.T., Yamapi, R.: Chaos synchronization of resistively coupled Duffing systems: numerical and experimental investigations. Commun. Nonlinear Sci. Numer. Simul. 14, 1439–1453 (2009)
Wu, C.L., Fang, T., Rong, H.W.: Chaos synchronization of two stochastic Duffing oscillators by feedback control. Chaos Solitons Fractals 32, 1201–1207 (2007)
Wu, X.F., Cai, J.P., Wang, M.H.: Global chaos synchronization of the parametrically excited duffing oscillators by linear state error feedback control. Chaos Solitons Fractals 36, 121–128 (2008)
Yin, J.L., Zhao, L.W.: Dynamic behaviors of the shock compacton in the nonlinearly Schrödinger equation with a source term. Phys. Lett. A 378, 3516–3522 (2014)
Acknowledgements
This work is supported by the National Nature Science Foundations of China (Nos. 11101191 and 71673116), the Natural Science Foundation of Jiangsu Province (No. SBK2015021674) and Jiangsu Qing Lan Project.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yin, J., Duan, X. & Tian, L. Optical secure communication modeled by the perturbed nonlinear Schrödinger equation. Opt Quant Electron 49, 317 (2017). https://doi.org/10.1007/s11082-017-1111-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-017-1111-7