Skip to main content
SpringerLink
Log in

New optical solitons of Tzitzeíca type evolution equations using extended trial approach

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

Abstract

The properties of Tzitzeíca equations in nonlinear optics have been the discussion of many recent studies. In this article, a new and productive implementation of trial equation method is chosen to handle this class of nonlinear evolution equations. As a result, the new and more exact periodic, singular, hyperbolic and rational solutions of Tzitzeíca, Dodd–Bullough–Mikhailov and Tzitzeíca–Dodd–Bullough equations are formally obtained. The extended trial equation method along with the symbolic computation gives a versatile technique to deal such kinds of nonlinear evolution equations in nonlinear optics.

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

  • Ablowitz, M.J., Clarkson, P.A.: Solitous Non-linear Evolution Equations and Inverse Scattering. Cambridge University Press, Cambridge (1991)

    Book  MATH  Google Scholar 

  • El-Sabbagh, M.F., El-Ganaini, S.I.: The first integral method and its applications to nonlinear equations. Appl. Math. Sci. 6, 3893–3906 (2012)

    MathSciNet  MATH  Google Scholar 

  • Fan, E.: Extended Tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277, 212–218 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Ferdi, Y.: Some applications of fractional oder calculus to design digital filters for biomedical signal processing. J. Mech. Med. Biol. 12, 13 (2013). https://doi.org/10.1142/s0219519412400088

    Google Scholar 

  • Gepreel, K.A.: Extended trial equation method for nonlinear coupled Schrodinger Boussinesq partial differential equations. J. Egypt. Math. Soc. 24, 381–391 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  • Guree, Y., Sonmezoglu, A., Misirli, E.: Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics. Pramana J. Phys. 77, 1023–1029 (2011)

    Article  ADS  Google Scholar 

  • Hosseini, K., Bekir, A., Kaplan, M.: New exact traveling wave solutions of the Tzitzeíca-type evolutions arising in non-linear optics. Mod. Opt. 64, 1688–1692 (2017a). https://doi.org/10.1080/09500340.2017.1302607

    Article  ADS  Google Scholar 

  • Hosseini, K., Ayati, Z., Ansari, R.: New exact traveling wave solutions of the Tzitzéica type equations using a novel exponential rational function method. Optik 148, 85–89 (2017b)

    Article  ADS  Google Scholar 

  • Khan, K., Akbar, M.: Exactand solitary wave solutions for the Tzitzeica–Dodd–Bullough and the modified KdV–Zakharov–Kuznetsov equations using the modified simple equation method. Ain Shams Eng. J. 4, 903–909 (2013)

    Article  Google Scholar 

  • Khan, K., Akbar, M.: Traveling wave solutions of the \((2+1)\)-dimensional Zoomeron equation and the Burgers equations via the MSE method and the Exp-function method. Ain Shams Eng. J. 5, 247–256 (2014a)

    Article  Google Scholar 

  • Khan, K., Akbar, M.: Exact solutions of the \((2+1)\)-dimensional cubic Klein-Gordon equation and the \((3+1)\)-dimensional Zakharov–Kuznetsov equation using the modified simple equation method. J. Assoc. Arab Univ. Basic Appl. Sci. 15, 74–81 (2014b)

    Google Scholar 

  • Khan, K., Akbar, M.: Traveling wave solutions of nonlinear evolution equations via the enhanced (G\(^\prime\)/G)-expansion method. J. Egypt. Math. Soc. 22, 220–226 (2014c)

    Article  MathSciNet  MATH  Google Scholar 

  • Khan, K., Akbar, M., Alam, M.: Traveling wave solutions of the non-linear Drinfeld–Sokolov–Wilson equation and modified Benjamin–Bona–Mahony equations. J. Egypt. Math. Soc. 21, 233–240 (2013)

    Article  MATH  Google Scholar 

  • Khan, K., Akbar, M., Roshid, H.: Exact traveling wave solutions of nonlinear evolution equation via enhanced (G\(^\prime\)/G)-expansion method. Br. J. Math. Comput. Sci. 4, 1318–1334 (2014)

    Article  Google Scholar 

  • Ma, W.X., Lee, J.H.: A transformed rational function method and exact solutions to the (3 + 1) dimensional Jimbo-Miwa equation. Chaos Solitons Fractals 42, 1356–1363 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Tarasova, V.V.: Fractional dynamics of natural growth and memory effect in economics. Eur. Res. 12, 30–37 (2016)

    Google Scholar 

  • Wang, M.L.: Solitary wave solutions for variant Boussinesq equations. Phys. Lett. A 199, 169–172 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Wang, Q., Tong, D.: The flow analysis of viscoelastic fluid with fractional oder derivative in horizontal well. Trans. Porous Med. 81, 295–303 (2010)

    Article  Google Scholar 

  • Wang, M., Zhou, Y., Li, Z.: Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Phys. Lett. A 216, 67–75 (1996)

    Article  ADS  MATH  Google Scholar 

  • Yan, C.T.: A simple transformation for nonlinear waves. Phys. Lett. A 224, 77–84 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan

    Nauman Raza & Muhammad Rizwan Aslam

  2. Lahore University of Management Sciences, Lahore Cantt, Pakistan

    Sultan Sial

Authors
  1. Nauman Raza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muhammad Rizwan Aslam
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sultan Sial
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nauman Raza.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Raza, N., Aslam, M.R. & Sial, S. New optical solitons of Tzitzeíca type evolution equations using extended trial approach. Opt Quant Electron 50, 141 (2018). https://doi.org/10.1007/s11082-018-1408-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-018-1408-1

Keywords

Search

Navigation