Advertisement

Exact optical solitons in metamaterials with anti-cubic law of nonlinearity by Lie group method

  • A. H. Abdel Kader
  • M. S. Abdel Latif
  • Qin ZhouEmail author
Article

Abstract

In this paper, using Lie point symmetry analysis, we study the dynamics of the solitons for the nonlinear Schrodinger’s equation with anti-cubic nonlinearity. Some new doubly periodic solutions are obtained that degenerate to dark and bright soliton solutions. In our of best knowledge, the obtained solutions are new. Those obtained results have important applications in the understanding the nonlinear propagation theory of solitons in metamaterials.

Keywords

Soliton solutions Schrodinger’s equation Lie symmetry analysis 

Notes

Acknowledgements

The work of Qin Zhou was supported by the National Natural Science Foundation of China (Grant Nos. 11705130 and 1157149) and by the Chutian Scholar Program of Hubei Government in China.

References

  1. Abdel Kader, A.H., Abdel Latif, M.S., Nour, H.M.: Exact solutions of a third-order ODE from thin film flow using λ-symmetry method. Int. J. Nonlinear Mech. 55, 147–152 (2013)CrossRefADSGoogle Scholar
  2. Abdel Kader, A.H., Abdel Latif, M.S., Nour, H.M.: General exact solution of the fin problem with the power law temperature-dependent thermal conductivity. Math. Methods Appl. Sci. 39, 1513–1521 (2016a)MathSciNetCrossRefADSGoogle Scholar
  3. Abdel Kader, A.H., Abdel Latif, M.S., Nour, H.M.: General exact solution of the fin problem with variable thermal conductivity. Propuls. Power Res. 5(1), 63–69 (2016b)CrossRefGoogle Scholar
  4. Abdel Kader, A.H., Abdel Latif, M.S., Nour, H.M.: Some new exact solutions of the modified kdv equation using lie point symmetry method. Int. J. Appl. Comput. Math. 3(Suppl 1), S1163–s1171 (2017a)MathSciNetCrossRefGoogle Scholar
  5. Abdel Kader, A.H., Abdel Latif, M.S., Bialy, F.E., Elsaid, A.: Symmetry analysis and some new exact solutions of some nonlinear KdV-like equations. Asian-Eur. J. Math. 11(3), 1850040 (2017b)MathSciNetCrossRefGoogle Scholar
  6. Abdel Latif, M.S., Abdel Kader, A.H., Nour, H.M.: Exact implicit solution of nonlinear heat transfer in rectangular straight fin using symmetry reduction methods. Appl. Appl. Math. 10(13), 864–877 (2015)MathSciNetzbMATHGoogle Scholar
  7. Afzal, S.S., Younis, M., Rizvi, S.T.R.: Optical dark and dark-singular solitons with anti-cubic nonlinearity. Optik 147, 27–31 (2017)CrossRefADSGoogle Scholar
  8. Biswas, A., Ekici, M., Sonmezoglu, A., Zhou, Q., Alshomrani, A.S., Moshokoa, S.P., Belic, M.: Solitons in optical metamaterials with anti-cubic nonlinearity. Eur. Phys. J. Plus 133(5), 204 (2018)CrossRefGoogle Scholar
  9. Ekici, M., Sonmezoglu, A., Zhou, Q., Moshokoa, S.P., Ullah, M.Z., Arnous, A.H., Belic, M.: Analysis of optical solitons in nonlinear negative-indexed materials with anti-cubic nonlinearity. Opt. Quantum Electron. 50(2), 75 (2018)CrossRefGoogle Scholar
  10. Foroutan, M., Manafian, J., Ranjbaran, A.: Solitons in optical metamaterials with anti-cubic law of nonlinearity by generalized G′/G-expansion method. Optik 162, 86–94 (2018a)CrossRefADSGoogle Scholar
  11. Foroutan, M., Manafian, J., Zamanpour, I.: Soliton wave solutions in optical metamaterials with anti-cubic law of nonlinearity by ITEM. Optik 164, 371–379 (2018b)CrossRefADSGoogle Scholar
  12. Guo, R., Hao, H.: Breathers and localized solitons for the Hirota–Maxwell–Bloch system on constant backgrounds in erbium doped fibers. Ann. Phys. 344, 10–16 (2014)CrossRefADSGoogle Scholar
  13. Guo, R., Hao, H., Zhang, L.: Dynamic behaviors of the breather solutions for the AB system in fluid mechanics. Nonlinear Dyn. 74, 701–709 (2013)MathSciNetCrossRefGoogle Scholar
  14. Hong, B., Lu, D.: New exact solutions for the generalized variable-coefficient Gardner equation with forcing term. Appl. Math. Comput. 219, 2732–2738 (2012)MathSciNetzbMATHGoogle Scholar
  15. Hydon, P.E.: Symmetry Methods for Differential Equations. Cambridge University Press, New York (2000)CrossRefGoogle Scholar
  16. Yang, Z., Zhang, S., Li, X., Pang, Z.: Variable sinh-Gaussian solitons in nonlocal nonlinear Schrödinger equation. Appl. Math. Lett. 82, 64–70 (2018)MathSciNetCrossRefADSGoogle Scholar
  17. Zhao, X., Guo, R., Hao, H.: N–fold Darboux transformation and discrete soliton solutions for the discrete Hirota equation. Appl. Math. Lett. 75, 114–120 (2018)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • A. H. Abdel Kader
    • 1
  • M. S. Abdel Latif
    • 1
  • Qin Zhou
    • 2
    Email author
  1. 1.Mathematics and Engineering Physics Department, Faculty of EngineeringMansoura UniversityMansouraEgypt
  2. 2.School of Electronics and Information EngineeringWuhan Donghu UniversityWuhanChina

Personalised recommendations