Skip to main content
SpringerLink
Log in

Extraction of optical solitons for nonlinear Biswas–Milovic equation in magneto-optic waveguide

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

A Correction to this article was published on 18 January 2024

This article has been updated

Abstract

In this study, the optical soliton solutions are extracted for the nonlinear Biswas–Milovic equation. The Biswas–Milovic equation is a coupled system in magneto-optic waveguide having Kudryashov’s law of refractive index. These equations have many applications in different branches of science, telecommunication industry, and technology. The exact optical soliton solutions are obtained by applying the \(\phi ^6\)-model expansion approach. This approach provides us the solutions in the form of Jacobi elliptic function, such as hyperbolic function solutions and trigonometric function solutions. The solutions are obtained in the form of dark soliton, bright soliton, periodic soliton, and singular soliton. Symbolic computations were used to validate all of the solutions obtained. In addition, some selected solutions are graphically described to demonstrate the physical characteristics of the gained solutions.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Data availability

Not applicable.

Change history

References

  • Abdou, M.A.: A generalized auxiliary equation method and its applications. Nonlinear Dyn. 52, 95–102 (2008)

    Article  MathSciNet  Google Scholar 

  • Ablowitz, M.J., Clarkson, P.A.: Solitons, nonlinear evolution equations and inverse scattering, vol. 149. Cambridge University Press, Cambridge (1991)

    Book  Google Scholar 

  • Baskonus, H.M., Bulut, H.: Analytical studies on the (1+ 1)-dimensional nonlinear dispersive modified Benjamin–Bona–Mahony equation defined by seismic sea waves. Waves Random Complex Media 25(4), 576–586 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  • Biswas, A.: Solitons in magneto-optic waveguides. Appl. Math. Comput. 153(2), 387–393 (2004)

    MathSciNet  Google Scholar 

  • Biswas, A., Milovic, D.: Bright and dark solitons of the generalized nonlinear Schrödinger’s equation. Commun. Nonlinear Sci. Numer. Simul. 15(6), 1473–1484 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  • Biswas, A., Jawad, A.J.A.M., Manrakhan, W.N., Sarma, A.K., Khan, K.R.: Optical solitons and complexitons of the Schrödinger-Hirota equation. Opt. Laser Technol. 44(7), 2265–2269 (2012)

    Article  ADS  Google Scholar 

  • Crutcher, S.H., Osei, A.: The modulated spatial Gausson solution to the Biswas–Milovic equation with log law nonlinearity. Optik 124(20), 4678–4681 (2013)

    Article  ADS  Google Scholar 

  • Dai, C.Q., Zhou, G.Q., Zhang, J.F.: Controllable optical rogue waves in the femtosecond regime. Phys. Rev. E 85(1), 016603 (2012)

    Article  ADS  Google Scholar 

  • Eslami, M., Mirzazadeh, M.: Optical solitons with Biswas–Milovic equation for power law and dual-power law nonlinearities. Nonlinear Dyn. 83, 731–738 (2016)

    Article  MathSciNet  Google Scholar 

  • Iqbal, M.S., Seadawy, A.R., Baber, M.Z.: Demonstration of unique problems from soliton solutions to nonlinear Selkov-Schnakenberg system. Chaos, Solitons Fractals 162, 112485 (2022)

    Article  MathSciNet  Google Scholar 

  • Kaur, L., Wazwaz, A.M.: Bright-dark optical solitons for Schrödinger-Hirota equation with variable coefficients. Optik 179, 479–484 (2019)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: Mathematical model of propagation pulse in optical fiber with power nonlinearities. Optik 212, 164750 (2020)

    Article  ADS  Google Scholar 

  • Kumar, S., Malik, S., Biswas, A., Zhou, Q., Moraru, L., Alzahrani, A.K., Belic, M.R.: Optical solitons with Kudryashov’s equation by Lie symmetry analysis. Phys. Wave Phenom. 28, 299–304 (2020)

    Article  ADS  Google Scholar 

  • Malik, S., Kumar, S.: Pure-cubic optical soliton perturbation with full nonlinearity by a new generalized approach. Optik 258, 168865 (2022)

    Article  CAS  ADS  Google Scholar 

  • Malik, S., Kumar, S., Biswas, A., Yildirim, Y., Moraru, L., Moldovanu, S., Alshehri, H.M.: Cubic-quartic optical solitons in fiber bragg gratings with dispersive reflectivity having parabolic law of nonlinear refractive index by lie symmetry. Symmetry 14(11), 2370 (2022)

    Article  ADS  Google Scholar 

  • Malik, S., Kumar, S., Biswas, A., Yildirim, Y., Moraru, L., Moldovanu, S., Alotaibi, A.: Gap solitons in fiber bragg gratings having polynomial law of nonlinear refractive index and cubic-quartic dispersive reflectivity by lie symmetry. Symmetry 15(5), 963 (2023)

    Article  ADS  Google Scholar 

  • Manafian, J.: On the complex structures of the Biswas–Milovic equation for power, parabolic and dual parabolic law nonlinearities. Eur. Phys. J. Plus 130(12), 255 (2015)

    Article  Google Scholar 

  • Rehman, H.U., Seadawy, A.R., Younis, M., Rizvi, S.T.R., Anwar, I., Baber, M.Z., Althobaiti, A.: Weakly nonlinear electron-acoustic waves in the fluid ions propagated via a (3+ 1)-dimensional generalized Korteweg-de-Vries-Zakharov-Kuznetsov equation in plasma physics. Results Phys. 33, 105069 (2022)

    Article  Google Scholar 

  • Rezazadeh, H., Mirhosseini-Alizamini, S.M., Eslami, M., Rezazadeh, M., Mirzazadeh, M., Abbagari, S.: New optical solitons of nonlinear conformable fractional Schrödinger-Hirota equation. Optik 172, 545–553 (2018)

    Article  ADS  Google Scholar 

  • Seadawy, A.R., Younis, M., Baber, M.Z., Rizvi, S.T., Iqbal, M.S.: Diverse acoustic wave propagation to confirmable time-space fractional KP equation arising in dusty plasma. Commun. Theor. Phys. 73(11), 115004 (2021)

    Article  MathSciNet  ADS  Google Scholar 

  • Seadawy, A.R., Bilal, M., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Analytical mathematical approaches for the double-chain model of DNA by a novel computational technique. Chaos, Solitons Fractals 144, 110669 (2021)

    Article  MathSciNet  Google Scholar 

  • Seadawy, A.R., Younis, M., Iqbal, M.S., Baber, M.Z., Rizvi, S.T., Raheem, A.: Soliton behavior of algae growth dynamics leading to the variation in nutrients concentration. J. King Saud Univ. Sci. 34(5), 102071 (2022)

    Article  Google Scholar 

  • Seadawy, A.R., Younis, M., Iqbal, M.S., Baber, M.Z., Rizvi, S.T., Raheem, A.: Soliton behavior of algae growth dynamics leading to the variation in nutrients concentration. J. King Saud Univ. Sci. 34(5), 102071 (2022)

    Article  Google Scholar 

  • Shahzad, T., Ahmad, M.O., Baber, M.Z., Ahmed, N., Ali, S.M., Akgül, A., Eldin, S.M.: Extraction of soliton for the confirmable time-fractional nonlinear Sobolev-type equations in semiconductor by ϕ6-modal expansion method. Results Phys. 46, 106299 (2023)

    Article  Google Scholar 

  • Soliman, A.A., Abdo, H.A.: New exact Solutions of nonlinear variants of the RLW, the PHI-four and Boussinesq equations based on modified extended direct algebraic method. (2012). arXiv preprint arXiv:1207.5127

  • Tuluce Demiray, S., Bulut, H.: Some exact solutions of generalized Zakharov system. Waves Random Complex Media 25(1), 75–90 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  • Yadav, R., Malik, S., Kumar, S., Sharma, R., Biswas, A., Yildirim, Y., Alghamdi, A.A.: Highly dispersive W-shaped and other optical solitons with quadratic-cubic nonlinearity: symmetry analysis and new Kudryashov’s method. Chaos Solitons Fractals 173, 113675 (2023)

    Article  MathSciNet  Google Scholar 

  • Younas, U., Ren, J.: Investigation of exact soliton solutions in magneto-optic waveguides and its stability analysis. Results Phys. 21, 103816 (2021)

    Article  Google Scholar 

  • Younas, U., Bilal, M., Ren, J.: Propagation of the pure-cubic optical solitons and stability analysis in the absence of chromatic dispersion. Opt. Quant. Electron. 53, 1–25 (2021)

    Article  Google Scholar 

  • Younas, U., Bilal, M., Sulaiman, T.A., Ren, J., Yusuf, A.: On the exact soliton solutions and different wave structures to the double dispersive equation. Opt. Quant. Electron. 54, 1–22 (2022)

    Article  Google Scholar 

  • Younis, M., Seadawy, A.R., Bilal, M., Rehman, S.U., Latif, S., Rizvi, S.T.R.: Kinetics of phase separation in Fe-Cr-X (X= Mo, Cu) ternary alloys-a dynamical wave study. Int. J. Mod. Phys. B 35(21), 2150220 (2021)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  • Zayed, E.M., Al-Nowehy, A.G.: The ϕ-model expansion method for solving the nonlinear conformable time-fractional Schrödinger equation with fourth-order dispersion and parabolic law nonlinearity. Opt. Quant. Electron. 50(3), 1–19 (2018)

    Article  Google Scholar 

  • Zayed, E.M., Gepreel, K.A., Shohib, R.M., Alngar, M.E.: Solitons in magneto-optics waveguides for the nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index using the unified auxiliary equation method. Optik 235, 166602 (2021)

    Article  CAS  ADS  Google Scholar 

  • Zhou, Q., Liu, L., Zhang, H., Wei, C., Lu, J., Yu, H., Biswas, A.: Analytical study of Thirring optical solitons with parabolic law nonlinearity and spatio-temporal dispersion. Eur. Phys. J. Plus 130, 1–6 (2015)

    Article  Google Scholar 

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Department of Basic Sciences and Humanities, University of Engineering and Technology Lahore, Narowal Campus, Lahore, 54890, Pakistan

    Tahir Shahzad

  2. Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

    Muhammad Zafarullah Baber, Muhammad Ozair Ahmad & Nauman Ahmed

  3. Department of Mathematics, Federal University Dutse, Jigawa, Nigeria

    Tukur Abdulkadir Sulaiman

  4. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Tukur Abdulkadir Sulaiman & Nauman Ahmed

  5. Operational Research Center in Healthcare, Near East University, TRNC Mersin 10, 99138, Nicosia, Turkey

    Tukur Abdulkadir Sulaiman

Authors
  1. Tahir Shahzad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muhammad Zafarullah Baber
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tukur Abdulkadir Sulaiman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Muhammad Ozair Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Nauman Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

TS: Formal analysis, Writing–original draft, Writing–review & editing. MZB: Conceptualization, Formal analysis, Writing–original draft, Writing–review & editing. TAS: Supervision, review & editing. MOA: Supervision, review & editing. NA: Conceptualization, Supervision, review & editing.

Corresponding author

Correspondence to Tukur Abdulkadir Sulaiman.

Ethics declarations

Conflict of interest

There is no competing interest whatsoever in this manuscript

Ethical approval

Not applicable.

Additional information

Publisher's Note

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

The original online version of this article was revised: The copyright holder for this article was incorrectly given.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) 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

Shahzad, T., Baber, M.Z., Sulaiman, T.A. et al. Extraction of optical solitons for nonlinear Biswas–Milovic equation in magneto-optic waveguide. Opt Quant Electron 56, 64 (2024). https://doi.org/10.1007/s11082-023-05531-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-023-05531-z

Keywords

Search

Navigation