Skip to main content
SpringerLink
Log in

Optical soliton perturbation for time fractional resonant nonlinear Schrödinger equation with competing weakly nonlocal and full nonlinearity

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

In this article, we retrieve optical soliton solutions of the perturbed time fractional resonant nonlinear Schrödinger equation having competing weakly nonlocal and full nonlinearity. We study the equation for two different forms of nonlinearity, namely Kerr law and anti-cubic law. The F-expansion method along with fractional complex transformation is used to obtain the optical solitons. Moreover, the existence of these solitons are guaranteed with the constraint relations between the model coefficients and the traveling wave frequency coefficient.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Abdullaev, F.K., Gammal, A., Tomio, L., Frederico, T.: Stability of trapped Bose-Einstein condensates. Phys. Rev. A 63, 043604 (2001)

    Article  ADS  Google Scholar 

  • Agrawal, G.P.: Nonlinear Fiber Optics. Academic Press, Cambridge (2001)

    MATH  Google Scholar 

  • Alshaery, A.A., Bhrawy, A.H., Hilal, A.E.M., Biswas, A.: Bright and singular solitons in quadratic nonlinear media. J. Electromagn. Waves Appl. 28(3), 275–280 (2014)

    Article  Google Scholar 

  • Bache, M., Bang, O., Krolikowski, W., Moses, J., Wise, F.W.: Limits to compression with cascaded quadratic soliton compressors. Opt. Express 16(5), 3273–3287 (2008)

    Article  ADS  Google Scholar 

  • Balykin, V.I., Hakuta, K., Kien, F., Liang, J.Q., Morinaga, M.: Atom trapping and guiding with subwavelength-diameter optical fiber. Phys. Rev. A 70, 011401 (R) (2004)

    Article  ADS  Google Scholar 

  • Bekir, A., Guner, Ö., Ünsal, Ö.: The first integral method for exact solutions of nonlinear fractional differential equations. J. Comput. Nonlinear Dyn. 10(2), 021020 (2015)

    Article  Google Scholar 

  • Benney, D.J., Newell, A.C.: The propagation of nonlinear wave envelope. J. Math. Phys. 46, 133–139 (1967)

    Article  MathSciNet  Google Scholar 

  • Biswas, A.: Optical solitons with time-dependent dispersion, nonlinearity and attenuation in a Kerr-law media. Int. J. Theor. Phys. 48, 256–260 (2009)

    Article  Google Scholar 

  • Biswas, A.: \(1\)-Soliton solution of the \(B(m, n)\) equation with generalized evolution. Commun. Nonlinear Sci. Numer. Simul. 14, 3226–3229 (2009)

    Article  ADS  Google Scholar 

  • Biswas, A., Konar, S.: Introduction to Non-Kerr Law Optical Solitons, pp. 1–212. CRC Press, Boca Raton (2006)

    MATH  Google Scholar 

  • Biswas, A., Milovic, D.: Chiral solitons with Bohm potential by He’s variational principle. Phys. At. Nuclei 74(5), 781–783 (2011)

    Article  Google Scholar 

  • Biswas, A., Kara, A.H., Zerrad, E.: Dynamics and conservation laws of the generalized chiral solitons. Open Nucl. Part. Phys. J. 4, 21–24 (2011)

    Article  ADS  Google Scholar 

  • Biswas, A., Fessak, M., Johnson, S., Beatrice, S., Milovic, D., Jovanoski, Z., Kohl, R., Majid, F.: Optical soliton perturbation in non-Kerr law media: traveling wave solution. Opt. Laser Technol. 44(1), 1775–1780 (2012)

    Article  Google Scholar 

  • Biswas, A., Fesssak, M., Johnson, S., Beatrice, S., Milovic, D., Jovanoski, Z., Kohl, R., Majid, F.: Optical soliton perturbation in non-Kerr law media: traveling wave solution. Opt. Laser Technol. 44(1), 1775–1780 (2012)

    Article  Google Scholar 

  • Biswas, A., Yildirim, Y., Yasar, E., Zhou, Q., Moshokoa, S.P., Belic, M.: Optical soliton perturbation with resonant nonlinear Schrödinger’s equation having full nonlinearity by modified simple equation method. Optik 160, 33–43 (2018)

    Article  ADS  Google Scholar 

  • Clerc, M.G., Couliblay, S., Gordillo, L., Mujica, N., Navarro, R.: Coalescence cascadeof dissipative solitons in parametrically driven systems. Phys. Rev. E 84, 036205 (2011)

    Article  ADS  Google Scholar 

  • Das, A.: Optical solitons for the resonant nonlinear Schrödinger equation with competing weakly nonlocal nonlinearity and fractional temporal evolution. Nonlinear Dyn. 90, 2231–2237 (2017)

    Article  Google Scholar 

  • Davydov, A.S.: Solitons in Molecular Systems, pp. 1–317. Reidel, Dordrecht (1985)

    Google Scholar 

  • Girgis, L., Milovic, D., Konar, S., Yildirim, A., Jafari, H., Biswas, A.: Optical Gaussonsin Birefringent fibers and DWDM systems with inter-modal dispersion. Rom. Rep. Phys. 64(3), 663–671 (2012)

    Google Scholar 

  • Hosseini, K., Ayati, Z.: Exact solutions of space-time fractional EW and modified EW equations using Kudryashov method. Nonlinear Sci. Lett. A 7(2), 58–66 (2016)

    Google Scholar 

  • Islam, W., Younis, M., Rizvi, S.T.R.: Optical solitons with time fractional nonlinear Schrödinger equation and competing weakly nonlocal nonlinearity. Optik 130, 562–567 (2017)

    Article  ADS  Google Scholar 

  • Jumarie, G.: Fractional Differential Calculus for Nondifferentiable Functions. Mechanics, Geometry, Stochastics, Information Theory, pp. 1–360. Lambert Academic Publishing, Saarbrucken (2013)

    Google Scholar 

  • Kharif, C., Pelinovsky, E., Slunyaev, A.: Rogue Waves in the Ocean, pp. 1–215. Springer, New York (2009)

    Book  Google Scholar 

  • Krolikowski, W., Bang, O.: Solitons in nonlocal nonlinear media: exact solutions. Phys. Rev. E 63, 016610 (2001)

    Article  ADS  Google Scholar 

  • Li, Z.B., He, J.H.: Fractional complex transform for fractional differential equations. Math. Comput. Appl. 15, 970–973 (2010)

    MathSciNet  MATH  Google Scholar 

  • Mohammed, A.F., Teik, C.H., Majumdar, S.P.: Limitations of soliton transmission in a cascaded optical amplifier system. J. Opt. Commun. 21(5), 165–170 (2000)

    Article  Google Scholar 

  • Pashaev, O.K., Lee, J.H.: Resonance solitons as black holes in Madelung fluid. Mod. Phys. Lett. A 17(24), 1601–1619 (2002)

    Article  ADS  Google Scholar 

  • Rizvi, S.T.R., Ali, K.: Jacobian elliptic periodic traveling wave solutions in the negative-index materials. Nonlinear Dyn. 87, 1967–1972 (2017)

    Article  Google Scholar 

  • Rogers, C., Yip, L.P., Chow, K.W.: A resonant Davey–Stewartson capillary model system. Int. J. Nonlinear Sci. Numer. Simul. 10(3), 397–405 (2009)

    Article  Google Scholar 

  • Triki, H., Hayat, T., Aldossary, O.M., Biswas, A.: Bright and dark solitons for the resonant nonlinear Schrödinger’s equation with time-dependent coefficients. Opt. Laser Technol. 44, 2223–2231 (2012)

    Article  ADS  Google Scholar 

  • Wang, M., Zhou, Y.: The periodic wave solutions for the Klein–Gordon–Schrödinger equations. Phys. Lett. A 318, 84–92 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  • Wang, M.L., Li, X.Z., Zheng, J.L.: The \((G^{\prime }/G)\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 372, 417–423 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  • Zheng, B.: \((G^{\prime }/G)\)-Expansion method for solving fractional partial differential equations in the theory of mathematical physics. Commun. Theor. Phys. (Beijing, China) 58, 623–630 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  • Zheng, B.: Exp-function method for solving fractional partial differential equations. Sci. World J. 2013, 465723 (2013)

    Google Scholar 

  • Zhou, Y., Wang, M., Wang, Y.: Periodic wave solutions to a coupled KdV equations with variable coefficients. Phys. Lett. A 308, 31–36 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  • Zhou, Q., Liu, L., Zhang, H., Mirzazadeh, M., Bhrawy, A.H., Zerrad, E., Moshokoa, S., Biswas, A.: Dark and singular optical solitons with competing nonlocal nonlinearities. Opt. Appl. 46(1), 79–86 (2016)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kalyani, Kalyani, 741235, India

    Amiya Das

Authors
  1. Amiya Das
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amiya Das.

Ethics declarations

Conflict of interest

The author declare that he has no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, A. Optical soliton perturbation for time fractional resonant nonlinear Schrödinger equation with competing weakly nonlocal and full nonlinearity. Opt Quant Electron 50, 376 (2018). https://doi.org/10.1007/s11082-018-1640-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-018-1640-8

Keywords

Search

Navigation