Log in

Invariant optical soliton solutions to the Coupled-Higgs equation

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

Abstract

In the present study, through the generalized exponential rational function method (GERFM), we construct optical soliton solution to the coupled-Higgs equation (CHE). The proposed method is one of the most powerful method to construct abundant exact solutions for nonlinear partial differential equations. The obtained wave solutions include hyperbolic, trigonometry, and exponential functions solutions. Furthermore, we draw three-dimensional surfaces and counter plots of the obtained solutions using the appropriate value for involved parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data availability

Data sharing is not applicable to this article as no data sets were generated or analyzed during the current study.

References

  • Ali, K.K., Yilmazer, R., Yokus, A., Bulut, H.: Analytical solutions for the (3+ 1)-dimensional nonlinear extended quantum Zakharov-Kuznetsov equation in plasma physics. Phys. A Stat. Mech. its Appl. 548, 124327 (2020). https://doi.org/10.1016/j.physa.2020.124327

    Article  MathSciNet  Google Scholar 

  • Ali, K.K., Resat Y., Osman, M.S.: Dynamic behavior of the (3 + 1)-dimensional KdV-Calogero-Bogoyavlenskii-Schiff equation. Opt. Quant. Electron. 54(3), 1–15 (2022).

  • Ali, K.K., Alireza K.G., Resat Y.: Battery discharging model on fractal time sets. Int. J. Nonlinear Sci. Numer. Simul. (2021). https://orcid.org/0000-0002-5008-0163

  • Ali, K.K., Resat Y., Osman, M.S.: Extended Calogero-Bogoyavlenskii-Schiff equation and its dynamical behaviors. Physica Scripta 96(12), 125249 (2021). https://doi.org/10.1088/1402-4896/ac35c5

  • Alquran, M., Al-Khaled, K.: Mathematical methods for a reliable treatment of the (2 + 1)-dimensional Zoomeron equation. Math. Sci. 6(1), 1–5 (2012).

    Article  Google Scholar 

  • Bulut, H., Akkilic, A.N., Khalid, B.J.: Soliton solutions of hirota equation and hirota-maccari system by the (m+ 1/G)-expansion method. Adv. Math. Models Appl. 6(1), 22–30 (2021).

    Google Scholar 

  • Bulut, H., Atas, S.S., Baskonus, H.M.: Some novel exponential function structures to the Cahn-Allen equation, Cogent. Phys. (2016). https://www.tandfonline.com/loi/oaph20

  • Gao, W., Ismael, H.F., Husien, A.M., Bulut, H., Baskonus, H.M.: Optical soliton solutions of the cubic-quartic nonlinear Schrödinger and resonant nonlinear Schrödinger equation with the parabolic law. Appl. Sci. 10(1), 219 (2020)

    Article  Google Scholar 

  • Ghanbari, B., Liu, J.-G.: Exact solitary wave solutions to the (2+ 1)-dimensional generalised Camassa-Holm-Kadomtsev-Petviashvili equation. Pramana 94(1), 1–11 (2020)

    Article  ADS  Google Scholar 

  • Gilding, B.H., Kersner, R.: Travelling waves in nonlinear diffusion-convection-reaction. University of Twente, 2001

  • Gu, C., Hu, H., Hu, A., Zhou, Z.: Darboux Transformations in Integrable Systems: Theory and their Applications to Geometry. Springer (2004)

  • Hafez, M.G., Alam, M.N., Akbar, M.A.: Traveling wave solutions for some important coupled nonlinear physical models via the coupled Higgs equation and the Maccari system. J. King Saud Univ. 27(2), 105–112 (2015).

    Article  Google Scholar 

  • Hirota, R., Satsuma, J.: Nonlinear evolution equations generated from the Bäcklund transformation for the Boussinesq equation. Prog. Theor. Phys. 57(3), 797–807 (1977).

    Article  ADS  Google Scholar 

  • Hu, X.-R., Chen, Y., Qian, L.-J.: Full symmetry groups and similar reductions of a (2+ 1)-dimensional resonant davey-stewartson system. Commun. Theor. Phys. 55(5), 737 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  • Idelsohn, S.R., Onate, E., Calvo, N., Del Pin, F.: The meshless finite element method. Int. J. Numer. Methods Eng. 58(6), 893–912 (2003)

    Article  MathSciNet  Google Scholar 

  • Inan, I.E., Bulut, H., Ataş, S.S., Yazgan, T.: Extended Exp(− φ(ξ))-Expansion Method for Some Exact Solutions of Sixth-Order Ramani Equation and Coupled Modified KdV-type Equation, Co-chair, p. 216

  • Islam, M., Barman, H.K., Akbar, M.A.: Search for interactions of phenomena described by the coupled Higgs field equation through analytical solutions. Opt. Quantum Electron. 52(11), 1–19 (2020).

    Article  Google Scholar 

  • Ismael, H.F., Atas, S.S., Bulut, H., Osman, M.S.: Analytical solutions to the M-derivative resonant Davey-Stewartson equations. Mod. Phys. Lett. B 35(30), 2150455 (2021). https://doi.org/10.1142/S0217984921504558

    Article  ADS  MathSciNet  Google Scholar 

  • Ismael, H.F., Bulut, H.: Multi soliton solutions, M-lump waves and mixed soliton-lump solutions to the awada-Kotera equation in (2+ 1)-dimensions. Chinese J. Phys. 71, 54–61 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  • Ismael, H.F., Bulut, H., Baskonus, H.M.: Optical soliton solutions to the Fokas-Lenells equation via sine-Gordon expansion method and (m + (G′/G))-expansion method. Pramana 94(1), 1–9 (2020).

    Article  Google Scholar 

  • Ismael, H.F., Ma, W.-X., Bulut, H.: Dynamics of soliton and mixed lump-soliton waves to a generalized Bogoyavlensky-Konopelchenko equation. Phys. Scr. 96(3), 35225 (2021). https://doi.org/10.1088/1402-4896/abdc55

    Article  Google Scholar 

  • Kumar, S., Singh, K., Gupta, R.K.: Coupled Higgs field equation and Hamiltonian amplitude equation: Lie classical approach and (G′/G)-expansion method. Pramana 79(1), 41–60 (2012)

    Article  ADS  Google Scholar 

  • Ma, W.-X., Abdeljabbar, A., Asaad, M.G.: Wronskian and Grammian solutions to a (3+ 1)-dimensional generalized KP equation. Appl. Math. Comput. 217(24), 10016–10023 (2011)

    MathSciNet  MATH  Google Scholar 

  • Ma, W.-X., Huang, T., Zhang, Y.: A multiple exp-function method for nonlinear differential equations and its application. Phys. Scr. 82(6), 65003 (2010). https://doi.org/10.1088/0031-8949/82/06/065003

    Article  Google Scholar 

  • Novikov, S., Manakov, S.V., Pitaevskii, L.P., Zakharov, V. E.: Theory of Solitons: the Inverse Scattering Method. Springer (1984)

  • Rezazadeh, H., Mirhosseini-Alizamini, S.M., Neirameh, A., Souleymanou, A., Korkmaz, A., Bekir, A.: Fractional Sine-Gordon equation approach to the coupled Higgs system defined in time-fractional form. Iran. J. Sci. Technol. Trans. A Sci. 43(6), 2965–2973 (2019)

    Article  MathSciNet  Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Ashraf, M.A., Bashir, A., Younis, M., Baleanu, D.: Multi-wave, homoclinic breather, M-shaped rational and other solitary wave solutions for coupled-Higgs equation. Eur. Phys. J. Spec. Top. 230(18), 3519–3532 (2021)

    Article  Google Scholar 

  • Scott, A.C.: Encyclopedia of Nonlinear Science. Routledge, New York (2005)

    MATH  Google Scholar 

  • Srivastava, H.M., et al.: Traveling wave solutions to nonlinear directional couplers by modified Kudryashov method. Phys. Scr. 95(7), 75217 (2020). https://doi.org/10.1088/1402-4896/ab95af

    Article  Google Scholar 

  • Sulaiman, T.A., Bulut, H., Atas, S.S.: Optical solitons to the fractional Schrdinger-Hirota equation. Appl. Math. Nonlinear Sci. 4(2), 535–542 (2019)

    Article  MathSciNet  Google Scholar 

  • Tarla, S., Karmina, K.A., Resat, Y., Osman, M.S.: New optical solitons based on the perturbed Chen-Lee-Liu model through Jacobi elliptic function method. Opt. Quant. Electron. 54(2), 1–12 (2022)

  • Yokus, A., Durur, H., Ahmad, H., Thounthong, P., Zhang, Y.-F.: Construction of exact traveling wave solutions of the Bogoyavlenskii equation by (G′/G)-expansion and (1/G)-expansion techniques. Results Phys. 19, 103409 (2020). https://doi.org/10.1016/j.rinp.2020.103409

    Article  Google Scholar 

Download references

Funding

This research receives no funding.

Author information

Authors and Affiliations

Authors

Contributions

This work was written with equal contributions from each author. The final manuscript was read and approved by all writers.

Corresponding author

Correspondence to Karmina K. Ali.

Ethics declarations

Conflict of interest

The authors declare that they have neither financial nor conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Atas, S.S., Ali, K.K., Sulaiman, T.A. et al. Invariant optical soliton solutions to the Coupled-Higgs equation. Opt Quant Electron 54, 754 (2022). https://doi.org/10.1007/s11082-022-04209-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-022-04209-2

Keywords

Navigation