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Chaotic behaviour from smooth and non-smooth optical solitons under external perturbation

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Abstract

Smooth and non-smooth optical solitons in the nonlinearly dispersive Schrödinger equation are given by phase portraits. The Melnikov technique is used to detect conditions for chaotic motion of this deterministic system and to analyse conditions for the suppression of chaos. Our results show that the system is in a state of Melnikov chaos by external disturbances. After the implementation of the controlled system, the optical solitons can transmit in a stable station for a long time. Numerical simulation also shows that maximum interference frequency of the system enables the dynamic behaviour to be more complex. The effect of controller parameter on phase portraits as well as on the numerical simulations of bifurcation diagram and maximum Lyapunov exponents are also investigated.

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References

  1. S Konar, M Mishra and Soumendu Jana, Phys. Lett. A 362, 505 (2007)

    Article  ADS  Google Scholar 

  2. M Mishra and S Konar, Progress Electromag. Res. 78, 301 (2008)

    Article  Google Scholar 

  3. M Mishra and S Konar, J. Electromag. Waves Appl. 21(14), 2049 (2007)

    Article  Google Scholar 

  4. S Jana and S Konar, Phys. Lett. A 362(5), 435 (2007)

    Article  ADS  Google Scholar 

  5. Semiha Ozgula, Meltem Turana, and Ahmet Yıldırıma, Optik 123, 2250 (2012)

    Article  Google Scholar 

  6. Jiuli Yin and Liuwei Zhao, Phys. Lett. A 378, 3516 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  7. Jiuli Yin, Liuwei Zhao and Lixin Tian, Melnikov’s criteria and chaos analysis in the nonlinear Schrödinger equation with Kerr law nonlinearity, Abs. Appl. Anal. Vol. 2014, Article ID 650781, 12 pages

  8. Jiuli Yin, Liuwei Zhao, and Lixin Tian, Chin. Phys. B 23(2), 020204 (2014)

    Google Scholar 

  9. G Yixiang and L Jibin, Appl. Math. Comput. 195, 420 (2008)

    MathSciNet  Google Scholar 

  10. Z Y Zhang, Z H Liu, X Z Miao, and Y Z Chen, Appl. Math. Comput. 216, 3064 (2010)

    MathSciNet  Google Scholar 

  11. H Moosaei, M Mirzazadeh, and A Yıldırım. ,Nonlinear Anal.: Model Control 16, 332 (2011)

    MATH  Google Scholar 

  12. P Masemola, A H Kara, and Anjan Biswas, Opt. Laser Technol. 45, 402 (2013)

    Article  ADS  Google Scholar 

  13. A R Shehata, Appl. Math. Comput. 217, 1 (2010)

    MathSciNet  Google Scholar 

  14. W Xiu Maa and M Chen, Appl. Math. Comput. 215, 2835 (2009)

    MathSciNet  Google Scholar 

  15. J B Beitia and G F Calvo, Phys. Lett. A 373, 448 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  16. X Jin Miao and Z Zai-yun, Commun. Nonlinear Sci. Numer. Simulat. 16, 4259 (2011)

    Article  ADS  Google Scholar 

  17. S Wiggins, Introduction to applied nonlinear dynamical systems and chaos (Springer-Verlag, New York, 1990)

    Book  MATH  Google Scholar 

  18. J Guckenheimer and P Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields (Springer-Verlag, New York, 2000)

    MATH  Google Scholar 

  19. D Jordan and P Smith, Nonlinear ordinary differential equations: An introduction for scientists and engineers (Oxford University Press, New York, 2007)

    MATH  Google Scholar 

  20. A Nayfeh and B Balachandran, Introduction to nonlinear dynamics: Analytical, computational, and experimental methods (Wiley, New York, 1995)

    MATH  Google Scholar 

  21. J Guckenheimer and P Homel, Nonlinear oscillations, dynamical system and bifurcation of vector fields (Springer-Verlag, 1992)

  22. Samuel C Stanton, Brian P Mann, and Benjamin A M Owens, Physica D 241, 711 (2012)

    Article  ADS  Google Scholar 

  23. V K Melnikov, Trans. Moscow Math. Soc. 12, 1 (1963)

    Google Scholar 

  24. J Awrejcewicz and Y Pyryev, Nonlinear Anal.: Real World Appl. 7, 12 (2006)

    Article  MathSciNet  Google Scholar 

  25. L Cveticanin and M Zukovic, J. Sound Vib. 326, 768 (2009)

    Article  ADS  Google Scholar 

  26. C A Kitio Kwuimy and B R Nana Nbendjo, Phys. Lett. A 375, 3442 (2011)

    Article  ADS  Google Scholar 

  27. L Cveticanin, Nonlin. Dynam. 4, 139 (1993)

    Google Scholar 

Download references

Acknowledgements

This work is supported by the National Nature Science Foundation of China (No. 11101191).

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Authors and Affiliations

  1. Social Science Computing Experiment Center, School of Management, Jiangsu University, Zhenjiang, Jiangsu, 212 013, China

    LIUWEI ZHAO

  2. Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, P R China

    LIUWEI ZHAO & JIULI YIN

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  1. LIUWEI ZHAO
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  2. JIULI YIN
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Correspondence to LIUWEI ZHAO.

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ZHAO, L., YIN, J. Chaotic behaviour from smooth and non-smooth optical solitons under external perturbation. Pramana - J Phys 87, 24 (2016). https://doi.org/10.1007/s12043-016-1215-9

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  • DOI: https://doi.org/10.1007/s12043-016-1215-9

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