Nonlinear Dynamics

, Volume 88, Issue 4, pp 2863–2872 | Cite as

Nematicons in liquid crystals by modified simple equation method

  • Ahmed H. Arnous
  • Malik Zaka Ullah
  • Mir Asma
  • Seithuti P. Moshokoa
  • Mohammad Mirzazadeh
  • Anjan Biswas
  • Milivoj Belic
Original Paper


This paper obtains nematicon solutions in liquid crystals by the aid of modified simple equation method. There are four types of nonlinearity studied. They are cubic law, power law, parabolic law and dual-power law. Bright, dark and singular types of these solitons are obtained. The constraints guarantee their existence.


Nematicons Liquid crystals Modified simple equation method 



The fourth author (SPM) would like to thank the research support provided by the Department of Mathematics and Statistics at Tshwane University of Technology and the support from the South African National Foundation under Grant Number 92052 IRF1202210126. The research work of seventh author (MB) was supported by Qatar National Research Fund (QNRF) under the Grant Number NPRP 6-021-1-005.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.


  1. 1.
    Arnous, A.H., Mirzazadeh, M., Zhou, Q., Mahmood, M.F., Biswas, A., Belic, M.: Optical solitons with resonant nonlinear Schrödinger’s equation using \(G^{\prime }/G\)-expansion scheme. Optoelectron. Adv. Mater. Rapid Commun. 9(9–10), 1214–1220 (2013)Google Scholar
  2. 2.
    Arnous, A.H., Mirzazadeh, M., Moshokoa, S., Medhekar, S., Zhou, Q., Mahmood, M.F., Biswas, A., Belic, M.: Solitons in optical metamaterials with trial solution approach and Bäcklund transform of Riccati equation. J. Comput. Theor. Nanosci. 12(12), 5940–5948 (2015)CrossRefGoogle Scholar
  3. 3.
    Arnous, A.H., Mirzazadeh, M., Zhou, Q., Moshokoa, S.P., Biswas, A., Belic, M.: Soliton solutions to resonant nonlinear Schrödinger’s equation with time-dependent coefficients by modified simple equation method. Optik 127(23), 11450–11459 (2016)CrossRefGoogle Scholar
  4. 4.
    Arnous, A.H., Ullah, M.Z., Moshokoa, S.P., Zhou, Q., Triki, H., Mirzazadeh, M., Biswas, A.: Optical solitons in birefringent fibers with modified simple equation method. Optik 130, 996–1003 (2017)CrossRefGoogle Scholar
  5. 5.
    El-Borai, M.M., El-Owaidy, H.M., Ahmed, H.M., Arnous, A.H., Moshokoa, S., Biswas, A., Belic, M.: Dark and singular optical solitons with spatio-temporal dispersion using modified simple equation method. Optik 130, 324–331 (2017)Google Scholar
  6. 6.
    Mirzazadeh, M., Arnous, A.H., Mahmood, M.F., Zerrad, E., Biswas, A.: Soliton solutions to resonant nonlinear Schrödinger’s equation with time-dependent coefficients by trial solution approach. Nonlinear Dyn. 81, 277–282 (2015)CrossRefMATHGoogle Scholar
  7. 7.
    Savescu, M., Johnson, S., Sanchez, P., Zhou, Q., Mahmood, M.F., Zerrad, E., Biswas, A., Belic, M.: Nematicons in liquid crystals. J. Comput. Theor. Nanosci. 12, 4667–4673 (2015)Google Scholar
  8. 8.
    Sciberras, L.W., Minzoni, A.A., Smyth, N.F., Assanto, G.: Steering of optical solitary waves by coplanar low power beams in reorientational media. J. Nonlinear Opt. Phys. Mater. 23(4), 1450045 (2014)CrossRefGoogle Scholar
  9. 9.
    Vega-Guzman, J., Mahmood, M.F., Zhou, Q., Triki, H., Arnous, A.H., Biswas, A., Moshokoa, S.P., Belic, M.: Solitons in nonlinear directional couplers with optical metamaterials. Nonlinear Dyn. 87(1), 427–458 (2017)CrossRefGoogle Scholar
  10. 10.
    Wazwaz, A.M.: Gaussian solitary wave solutions for nonlinear evolution equations with logarithmic nonlinearities. Nonlinear Dyn. 83(1), 591–596 (2016)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Wazwaz, A.M.: Multiple soliton solutions and multiple complex soliton solutions for two distinct Boussinesq equations. Nonlinear Dyn. 85(2), 731–737 (2016)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Wazwaz, A.M., El-Tantawy, S.A.: A new (\(3+1\))-dimensional generalized Kadomtsev Petviashvili equation. Nonlinear Dyn. 84(2), 1107–1112 (2016)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Wazwaz, A.M., Xu, G.Q.: An extended modified KdV equation and its Painlev integrability. Nonlinear Dyn. 86(3), 1455–1460 (2016)CrossRefGoogle Scholar
  14. 14.
    Wazwaz, A.M.: Two-mode fifth-order KdV equations: necessary conditions for multiple-soliton solutions to exist. Nonlinear Dyn. 87(3), 1685–1691 (2017)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Zayed, E.M.E., Arnous, A.H.: Exact solutions of the nonlinear ZK-MEW and the potential YTSF equations using the modified simple equation method. AIP Conf. Proc. 1479, 2044–2048 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Ahmed H. Arnous
    • 1
  • Malik Zaka Ullah
    • 2
  • Mir Asma
    • 3
  • Seithuti P. Moshokoa
    • 4
  • Mohammad Mirzazadeh
    • 5
  • Anjan Biswas
    • 2
    • 4
  • Milivoj Belic
    • 6
  1. 1.Department of Engineering Mathematics and PhysicsHigher Institute of EngineeringEl-ShoroukEgypt
  2. 2.Operator Theory and Applications Research Group, Department of MathematicsFaculty of Science, King Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Institute of Mathematical Sciences, Faculty of ScienceUniversity of MalayaKuala LumpurMalaysia
  4. 4.Department of Mathematics and StatisticsTshwane University of TechnologyPretoriaSouth Africa
  5. 5.Department of Engineering Sciences, Faculty of Technology and Engineering, East of GuilanUniversity of GuilanRudsar-VajargahIran
  6. 6.Science ProgramTexas A&M University at QatarDohaQatar

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