Nonlinear Dynamics

, Volume 87, Issue 3, pp 1967–1972 | Cite as

Jacobian elliptic periodic traveling wave solutions in the negative-index materials

  • Syed Tahir Raza Rizvi
  • Kashif Ali
Original Paper


The aim of this work is to present an analytical study on optical solitons in nonlinear negative-index materials. Three types of nonlinearities that are Kerr law, power law and parabolic law are taken into account. With the help of F-expansion method, the explicit Jacobian elliptic periodic traveling wave solutions are constructed.


Solitons Negative-index materials Power-law nonlinearity F-expansion method 


  1. 1.
    Zhou, Q., Liu, L., Liu, Y., Yu, H., Yao, P., Wei, C., Zhang, H.: Exact optical solitons in metamaterials with cubic quintic nonlinearity and third-order dispersion. Nonlinear Dyn. 80(3), 1365–1371 (2015)CrossRefGoogle Scholar
  2. 2.
    Biswas, A., Khan, K.R., Mahmood, M.F.: Bright and dark solitons in optical metamaterials. Optik 125(3), 3299–3302 (2014)CrossRefGoogle Scholar
  3. 3.
    Xu, Y., Savescu, M., Khan, K.R., Mahmood, M.F., Biswas, A., Belic, M.: Soliton propagation through nanoscale waveguides in optical metamaterials. Opt. Laser Technol. 77, 177–186 (2016)CrossRefGoogle Scholar
  4. 4.
    Saha, M., Sarma, A.K.: Modulation instability in nonlinear metamaterials induced by cubic-quintic nonlinearities and higher order dispersive effects. Opt. Commun. 291, 321–325 (2013)CrossRefGoogle Scholar
  5. 5.
    Yang, R., Zhang, Y.: Exact combined solitarywave solutions 651 in nonlinear metamaterials. J. Opt. Soc. Am. B 28(1), 123–127 (2011)CrossRefGoogle Scholar
  6. 6.
    Savescu, M., Zhou, Q., Moraru, L., Biswas, A., Moshokoa, S.P., Belic, M.: Singular optical solitons in birefringent nano-fibers. Optik Int. J. Light Electron Opt. 127(20), 8995–9000 (2016)CrossRefGoogle Scholar
  7. 7.
    Zhou, Q., Mirzazadeh, M., Ekici, M., Sonmezoglu, A.: Analytical study of solitons in non-Kerr nonlinear negative-index materials. Nonlinear Dyn. 86(1), 623–638 (2016)Google Scholar
  8. 8.
    Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M., Eslami, M.: Analytical study of solitons to Biswas–Milovic model in nonlinear optics. J. Mod. Opt. 63(21), 2131–2137 (2016)Google Scholar
  9. 9.
    Zhou, Q.: Optical solitons for Biswas–Milovic model with Kerr law and parabolic law nonlinearities. Nonlinear Dyn. 84(2), 677–681 (2016)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Zhou, Q.: Analytical 1-solitons in a nonlinear medium with higher-order dispersion and nonlinearities. Waves Random Complex Media 26(2), 197–203 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Kumar, S., Zhou, Q., Biswas, A., Belic, M.: Optical solitons in nano-fibers with Kundu–Eckhaus equation by Lie symmetry analysis. Optoelectron. Adv. Mater. Rapid Commun. 10(1–2), 21–24 (2016)Google Scholar
  12. 12.
    Zhou, Q.: Soliton and soliton-like solutions to the modified Zakharov–Kuznetsov equation in nonlinear transmission line. Nonlinear Dyn. 83(3), 1429–1435 (2016)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Zhou, Q.: Analytical study of solitons in magneto-electro-elastic circular rod. Nonlinear Dyn. 83(3), 1403–1408 (2016)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Liu, S.S., Liu, S.D.: Nonlinear Equations in Physics. Peking University Press, Beijing (2002)Google Scholar
  15. 15.
    Ebadi, G., Mojavir, A., Guzman, J.V., Khan, K.R., Mahmood, M.F., Moraru, L., Biswas, A., Belic, M.: Solitons in optical metamaterials by \(F\)-expansion scheme. Optoelectron Adv Mater Rapid Commun 8, 828–832 (2014)Google Scholar
  16. 16.
    Filiz, A., Ekici, M., Sonmezoglu, A.: \(F\)-Expansion method and new exact solutions of the Schrdinger–KdV equation. Sci. World J. (2014). doi: 10.1155/2014/534063

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of MathematicsCOMSATS Institute of Information TechnologyLahorePakistan

Personalised recommendations