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Optical secure communication modeled by the perturbed nonlinear Schrödinger equation

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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.

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References

  • Ahn, C.K.: A new chaos synchronization method for Duffing oscillator. IEICE Electr. Expr. 6, 1355–1360 (2009)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  ADS  MATH  Google Scholar 

  • Mathieu, C., Masahito, O.: Instability of ground states for a quaslinear Schrödinger equation. Differ. Integral Equ. 27, 613–624 (2014)

    MATH  Google Scholar 

  • Nottale, L.: Generalized quantum potentials. J. Phys. A Math. Theor. 42, 275306 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Wang, B.X., Guan, Z.H.: Chaos synchronization in general complex dynamical networks withcoupling delays. Nonlinear Anal. Real World Appl. 11, 1925–1932 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Wang, S.B., Wang, X.Y., Zhou, Y.: A memristor-based complex Lorenz system and its modified projective synchronization. Entropy 17, 7628–7644 (2015)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  MATH  Google Scholar 

  • 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)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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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.

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Correspondence to Jiuli Yin.

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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

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  • DOI: https://doi.org/10.1007/s11082-017-1111-7

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