Advertisement

Dispersive bright, dark and singular optical soliton solutions in conformable fractional optical fiber Schrödinger models and its applications

  • M. T. Darvishi
  • M. Najafi
  • Aly R. Seadawy
Article
  • 75 Downloads

Abstract

In this paper, we study three different space-time fractional models of the Schrödinger equation. By using the properties of conformable derivative and fractional complex transform, the bright, dark and singular optical solitons for conformable space–time fractional nonlinear \((1+1)\)-dimensional Schrödinger models are determined.

Keywords

Schrödinger models Bright–dark soliton Singular soliton Conformable fractional derivative 

References

  1. Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  2. Abdullaha, A., Seadawy, A.R., Jun, W.: Mathematical methods and solitary wave solutions of three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma and its applications. Results Phys. 7, 4269–4277 (2017)ADSCrossRefGoogle Scholar
  3. Agrawal, G.P.: Nonlinear fiber optics: its history and recent progress [Invited]. J. Opt. Soc. America B 28, A1–A10 (2011)ADSCrossRefGoogle Scholar
  4. Arshad, M., Seadawy, Aly R., Lu, Dianchen: Exact bright-dark solitary wave solutions of the higher-order cubic-quintic nonlinear Schrödinger equation and its stability, Optik 128, 40–49 (2017)ADSCrossRefGoogle Scholar
  5. Darvishi, M.T., Ahmadian, S., Baloch Arbabi, S., Najafi, M.: Optical solitons for a family of nonlinear (1+1)-dimensional time-space fractional Schrödinger models. Opt. Quantum Electron. 50, 1–20 (2018)CrossRefGoogle Scholar
  6. Eslami, M., Rezazadeh, H., Rezazadeh, M., Mosavi, S.S.: Exact solutions to the space-time fractional Schrödinger-Hirota equation and the space-time modified KDV-Zakharov-Kuznetsov equation . Opt. Quantum Electron. 49, 1–13 (2017)CrossRefGoogle Scholar
  7. Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  8. Kumar, H., Chand, F: Dark and bright solitary wave solutions Of the higher order nonlinear Schröodinger equation with self-steepening and Self-frequency shift effects. J. Nonlinear Opt Phys. Mater. 22, 1–8 (2013)CrossRefGoogle Scholar
  9. Kumar, D., Darvishi, M.T., Joardar, A.K.: Modified Kudryashov method and its application to the fractional version of the variety of Boussinesq-like equations in shallow water. Opt. Quantum Electron. 50, 1–18 (2018)CrossRefGoogle Scholar
  10. Kumar, D., Seadawy, A.R., Joardar, A.K.: Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology. Chinese Journal of Physics 56, 75–85 (2018)ADSCrossRefGoogle Scholar
  11. Kurt, A., Tasbozan, O., Baleanu, D.: New solutions for conformable fractional Nizhnik-Novikov-Veselov system via \((\frac{G^{\prime }}{G})\)-expansion method and homotopy analysis method. Opt. Quantum Electron. 49, 1–10 (2017)CrossRefGoogle Scholar
  12. Lu, Dianchen, Seadawy, A.R., Arshad, M.: Bright-dark solitary wave and elliptic function solutions of unstable nonlinear Schr\({\ddot{o}}\)dinger equation and their applications. Opt. Quantum Electron 50, 23 (2018).  https://doi.org/10.1007/s11082-017-1294-y CrossRefGoogle Scholar
  13. Pawlik, M., Rowlands, G.: The propagation of solitary waves in piezoelectric semiconductors. J. Phys. C 8, 1189–1204 (1975)ADSCrossRefGoogle Scholar
  14. Pedlosky, V.E.: Finite-amplitude baroclinic waves. J. Atmos. Sci. 27, 15–30 (1970)ADSCrossRefGoogle Scholar
  15. Seadawy, A.R.: Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods. Eur. Phys. J. Plus 132, 518 (2017).  https://doi.org/10.1140/epjp/i2017-11755-6 CrossRefGoogle Scholar
  16. Seadawy, A.R., El-Rashidy, K.: Traveling wave solutions for some coupled nonlinear evolution equations. Mathematical and Computer Modelling 57, 1371–1379 (2013)MathSciNetCrossRefGoogle Scholar
  17. Wazwaz, A.M.: A study on linear and nonlinear Schrödinger equations by the variational iteration method. Chaos Solitons Fractals 37, 1136–1142 (2008)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. Zhang, W.: Generalized variational principle for long water-wave equation by He’s semi-inverse method. Math. Probl. Eng. 2009, 1–6 (2009)ADSMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsRazi UniversityKermanshahIran
  2. 2.Mathematics Department, Faculty of ScienceTaibah UniversityAl-Madinah Al-MunawarahSaudi Arabia
  3. 3.Mathematics Department, Faculty of ScienceBeni-Suef UniversityBeni SuefEgypt

Personalised recommendations