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Control of interaction between femtosecond dark solitons in inhomogeneous optical fibers

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Abstract

In this paper, we present exact femtosecond one- and two-dark soliton solutions for a variable-coefficient higher-order nonlinear Schrödinger equation via modified Hirota method. The propagation and interaction of femtosecond dark solitons are investigated in inhomogeneous fiber systems. Elastic collision, bound oscillation and parallel propagation can be achieved in both Gaussian distributed parameter system and exponentially periodic distributed parameter system by choosing the appropriate distributed parameters and soliton parameters. The results may be beneficial to the realization of interaction control of femtosecond dark solitons in communication systems.

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References

  • Agrawal, G.P.: Nonlinear Fiber Optics, 3rd edn. Academic Press, New York (2001)

    MATH  Google Scholar 

  • Amiri, I.S., Naraei, P., Ali, J.: Review and theory of optical soliton generation used to improve the security and high capacity of MRR and NRR passive systems. J. Comput. Theor. Nanos. 11(9), 1875–1886 (2014)

    Article  Google Scholar 

  • Bogatyrev, V.A., Bubnov, M.M., Dianov, E.M., Kurkov, A.S., Mamyshev, P.V.: A single-mode fiber with chromatic dispersion varying along the length. J. Lightw. Technol. 9(5), 561–566 (1991)

    Article  ADS  Google Scholar 

  • Choudhuri, A., Triki, H., Porsezian, K.: Self-similar localized pulses for the nonlinear Schrödinger equation with distributed cubic-quintic nonlinearity. Phys. Rev. A (2016). https://doi.org/10.1103/PhysRevA.94.063814

    Google Scholar 

  • Dai, C.Q., Zhang, J.F.: New solitons for the Hirota equation and generalized higher-order nonlinear Schrödinger equation with variable coefficients. J. Phys. A Math. Gen. 39, 723–737 (2006)

    Article  ADS  MATH  Google Scholar 

  • Dai, C.Q., Xu, Y.J., Wang, Y.: Nonautonomous cnoidal wave and soliton management in parity-time symmetric potentials. Commun. Nonlin. Sci. Numer. Simulat. 20(2), 389–400 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Feng, Y.J., Gao, Y.T., Sun, Z.Y., Zuo, D.W., Shen, Y.J., Sun, Y.H., Xue, L., Yu, X.: Anti-dark solitons for a variable-coefficient higher-order nonlinear Schrödinger equation in an inhomogeneous optical fiber. Phys. Scr. (2015). https://doi.org/10.1088/0031-8949/90/4/045201

    Google Scholar 

  • Gordon, J.P.: Interaction forces among solitons in optical fibers. Opt. Lett. 8(11), 596–598 (1983)

    Article  ADS  Google Scholar 

  • Gumenyuk, R., Okhotnikov, O.G.: Impact of gain medium dispersion on stability of soliton bound states in fiber laser. IEEE Photon. Technol. Lett. 25(50), 454–456 (2013)

    Article  ADS  Google Scholar 

  • Hao, R.Y., Li, L., Li, Z.H., Zhou, G.S.: Exact multisoliton solutions of the higher-order nonlinear Schrödinger equation variable coefficients. Phys. Rev. E (2004). https://doi.org/10.1103/PhysRevE.70.066603

    Google Scholar 

  • Hirota, R.: Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27(18), 1192–1194 (1971)

    Article  ADS  MATH  Google Scholar 

  • Kivshar, Y.S., Agrawal, G.P.: Optical solitons: from fibers to photonic crystals. Academic Press, San Diego (2003)

    Google Scholar 

  • Kruglov, V.I., Peacock, A.C., Harvey, J.D.: Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients. Phys. Rev. Lett. 90(11), 113902 (2003)

    Article  ADS  Google Scholar 

  • Liu, W.J., Pang, L.H., Han, H.N., Tian, W.L., Chen, H., Lei, M., Yan, P.G., Wei, Z.Y.: Generation of dark solitons in erbium-doped fiber lasers based Sb2Te3 saturable absorbers. Opt. Express 23(20), 26023–26031 (2015)

    Article  ADS  Google Scholar 

  • Liu, W.J., Huang, L.G., Huang, P., Li, Y.Q., Lei, M.: Dark soliton control in inhomogeneous optical fibers. Appl. Math. Lett. 61, 80–87 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  • Malomed, B.A.: Soliton management in periodic systems. Springer, New York (2006)

    MATH  Google Scholar 

  • Mani Rajan, M.S.: Dynamics of optical soliton in a tapered erbium-doped fiber under periodic distributed amplification system. Nonlinear Dyn. 85, 599–606 (2016)

    Article  Google Scholar 

  • Mani Rajan, M.S., Mahalingam, A.: Nonautonomous solitons in modified inhomogeneous Hirota equation: soliton control and soliton interaction. Nonlinear Dyn. 79, 2469–2484 (2015)

    Article  MathSciNet  Google Scholar 

  • Nimmo, J.J.C., Freeman, N.C.: The use of Bäcklund transformations in obtaining N-soliton solutions in Wronskian form. J. Phys. A Math. Gen. 17(7), 1415–1424 (1984)

    Article  ADS  MATH  Google Scholar 

  • Serkin, V.N., Belyaeva, T.L.: Optimal Control of soliton parameters: Part 1. The Lax representation in the problem of soliton management. Quantum Electron. 31(11), 1007–1015 (2001)

    Article  ADS  Google Scholar 

  • Serkin, V.N., Hasegawa, A.: Exactly integrable nonlinear Schrödinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion managements. IEEE. J. Sel. Top. Quant. 8(3), 418–431 (2002)

    Article  Google Scholar 

  • Song, X.H., Yang, C.Y., Yu, W.T., Zhang, Y.J., Liu, M.L., Lei, M., Liu, W.J.: Inelastic interaction between dark solitons for fourth-order variable-coefficient nonlinear Schrödinger equation. J. Electromagn. Wave. 31, 762–767 (2017)

    Article  Google Scholar 

  • Subramanian, K., Alagesan, T., Mahalingam, A., Mani Rajan, M.S.: Propagation properties of optical soliton in an erbium-doped tapered parabolic index nonlinear fiber: soliton control. Nonlinear Dyn. 87, 1575–1587 (2017)

    Article  Google Scholar 

  • Sun, Y., Tian, B., Wu, X.Y., Liu, L., Yuan, Y.Q.: Dark solitons for a variable-coefficient higher-order nonlinear Schrödinger equation in the inhomogeneous optical fiber. Mod. Phys. Lett. B (2017). https://doi.org/10.1142/S0217984917500658

    Google Scholar 

  • Tian, B., Gao, Y.T., Zhu, H.W.: Variable-coefficient higher-order nonlinear Schrödinger model in optical fibers: variable-coefficient bilinear form, Bäcklund transformation, brightons and symbolic computation. Phys. Lett. A 366, 223–229 (2007)

    Article  ADS  MATH  Google Scholar 

  • Wong, P., Liu, W.J., Huang, L.G., Li, Y.Q., Pan, N., Lei, M.: Higher-order-effects management of soliton interactions in the Hirota equation. Phys. Rev. E (2015). https://doi.org/10.1103/PhysRevE.91.033201

    MathSciNet  Google Scholar 

  • Yang, R.C., Hao, R.Y., Li, L., Li, Z.H., Zhou, G.S.: Dark soliton solution for higher-order nonlinear Schrödinger equation with variable coefficients. Opt. Commum. 242, 285–293 (2004)

    Article  ADS  Google Scholar 

  • Yang, R.C., Hao, R.Y., Li, L., Shi, X.J., Li, Z.H., Zhou, G.S.: Exact gray multi-soliton solutions for nonlinear Schrödinger equation with variable coefficients. Opt. Commum. 253, 177–185 (2005a)

    Article  ADS  Google Scholar 

  • Yang, R.C., Li, L., Hao, R.Y., Li, Z.H., Zhou, G.S.: Combined solitary wave solutions for the inhomogeneous higher-order nonlinear Schrödinger equation. Phys. Rev. E (2005b). https://doi.org/10.1103/PhysRevE.71.036616

    Google Scholar 

  • Yang, J.W., Gao, Y.T., Feng, Y.J., Su, C.Q.: Solitons and dromion-like structures in an inhomogeneous optical fiber. Nonlinear Dyn. 87, 851–862 (2017)

    Article  Google Scholar 

  • Zhao, W., Bourkoff, E.: Interactions between dark solitons. Opt. Lett. 14(24), 1371–1373 (1989)

    Article  ADS  Google Scholar 

  • Zhao, C., Gao, Y.T., Lan, Z.Z., Yang, J.W., Su, C.Q.: Bilinear forms and dark-soliton solutions for a fifth-order variable-coefficient nonlinear Schrödinger equation in an optical fiber. Mod. Phys. Lett. B (2016). https://doi.org/10.1142/S0217984916503127

    Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant Numbers 61775126, 61771295); Natural Science Foundation of Shanxi Province (Grant Number 2016011038); Shanxi “1331 Project” Key Subjects Construction (1331KSC).

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Correspondence to Rongcao Yang.

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Gao, J., Yang, R., Tian, J. et al. Control of interaction between femtosecond dark solitons in inhomogeneous optical fibers. Opt Quant Electron 50, 286 (2018). https://doi.org/10.1007/s11082-018-1537-6

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