Skip to main content
SpringerLink
Log in

Explicit solitons in the parabolic law nonlinear negative-index materials

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper deals with the existence of explicit ultra-short solitons in the negative-index materials with third-order dispersion and higher-order nonlinearities. Four integration algorithms, that are the improved modified extended tanh-function method, the extended trial equation method, the extended Jacobi elliptic function expansion method and the \(\exp \left( -\Phi \left( \eta \right) \right) \)-expansion method, are employed to extract analytical traveling wave solutions. The presented results show that exact solitons can exist in this physical model.

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

Similar content being viewed by others

References

  1. Xiang, Y., Dai, X., Wen, S., Guo, J., Fan, D.: Controllable Raman soliton self-frequency shift in nonlinear metamaterials. Phys. Rev. A 84, 033815 (2011)

    Article  Google Scholar 

  2. Yang, R., Zhang, Y.: Exact combined solitary wave solutions in nonlinear metamaterials. J. Opt. Soc. Am. B 28, 123–127 (2011)

    Article  Google Scholar 

  3. Biswas, A., Khan, K.R., Mahmood, M.F.: Bright and dark solitons in optical metamaterials. Optik 125, 3299–3302 (2014)

    Article  Google Scholar 

  4. 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, 1365–1371 (2015)

    Article  Google Scholar 

  5. Zhou, Q., Mirzazadeh, M., Ekici, M., Sonmezoglu, A.: Analytical study of solitons in non-Kerr nonlinear negative-index materials. Nonlinear Dyn. 86, 623–638 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  6. Yang, Z., Hon, B.Y.C.: An improved modified extended tanh-function method. Z. Naturforsch 61a, 103–115 (2006)

  7. Jiong, S.: Auxiliary equation method for solving nonlinear partial differential equations. Phys. Lett. A. 309, 387–396 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Liu, C.: Representations and classification of traveling wave solutions to sinh-Gordon equation. Commun. Theor. Phys. 49(1), 153 (2008)

    Article  MathSciNet  Google Scholar 

  9. Liu, C.: Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations. Comput. Phys. Commun. 181(2), 317–324 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ekici, M., Mirzazadeh, M., Eslami, M.: Solitons and other solutions to Boussinesq equation with power law nonlinearity and dual dispersion. Nonlinear Dyn. 84(2), 669–676 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M., Eslami, M.: Optical solitons with Biswas–Milovic equation by extended trial equation method. Nonlinear Dyn. 84(4), 1883–1900 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Gurefe, Y., Misirli, E., Sonmezoglu, A., Ekici, M.: Extended trial equation method to generalized nonlinear partial differential equations. Appl. Math. Comput. 219, 5253–5260 (2013)

    MathSciNet  MATH  Google Scholar 

  13. Huiqun, Z.: Extended Jacobi elliptic function expansion method and its applications. Commun. Nonlinear Sci. Numer. Simul. 12, 627–635 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Abdou, M.A., Elhanbaly, A.: Construction of periodic and solitary wave solutions by the extended Jacobi elliptic function expansion method. Nonlinear Sci. Numer. Simul. 12, 1229–1241 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Bhrawy, A.H., Abdelkawy, M.A., Biswas, A.: Cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended Jacobis elliptic function method. Commun. Nonlinear Sci. Numer. Simul. 18, 915–925 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mirzazadeh, M., Ekici, M., Sonmezoglu, A., Ortakaya, S., Eslami, M., Biswas, A.: Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics. Eur. Phys. J. Plus 131, 166 (2016)

    Article  Google Scholar 

  17. Khan, K., Akbar, M.A.: Application of \(\exp \left(-\Phi \left(\xi \right)\right)\)-expansion method to find the exact solutions of modified Benjamin–Bona–Mahony equation. World Appl. Sci. J. 24(10), 1373–1377 (2013)

    Google Scholar 

  18. Roshid, H.O., Kabir, M.R., Bhowmik, R.C., Datta, B.K.: Investigation of solitary wave solutions for Vakhnenko–Parkes equation via exp-function and \(\exp \left(-\Phi \left(\xi \right)\right)\)-expansion method. SpringerPlus 3, 692 (2014)

    Article  Google Scholar 

  19. Guo, R., Liu, Y.F., Hao, H.Q., Qi, F.H.: Coherently coupled solitons, breathers and rogue waves for polarized optical waves in an isotropic medium. Nonlinear Dyn. 80, 1221–1230 (2015)

    Article  MathSciNet  Google Scholar 

  20. Lü, X.: Madelung fluid description on a generalized mixed nonlinear Schrödinger equation. Nonlinear Dyn. 81, 239–247 (2015)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  22. Dai, C.Q., Wang, Y.Y.: Spatiotemporal localizations in (3+1)-dimensional PT-symmetric and strongly nonlocal nonlinear media. Nonlinear Dyn. 83, 2453–2459 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under the Grant Number 11547149.

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100, Yozgat, Turkey

    Abdullah Sonmezoglu & Mehmet Ekici

  2. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, People’s Republic of China

    Min Yao & Qin Zhou

  3. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, P.C. 44891-63157, Iran

    Mohammad Mirzazadeh

Authors
  1. Abdullah Sonmezoglu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Min Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mehmet Ekici
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohammad Mirzazadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Qin Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qin Zhou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sonmezoglu, A., Yao, M., Ekici, M. et al. Explicit solitons in the parabolic law nonlinear negative-index materials. Nonlinear Dyn 88, 595–607 (2017). https://doi.org/10.1007/s11071-016-3263-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-3263-6

Keywords

Search

Navigation