Skip to main content
SpringerLink
Log in

Dynamics of solitons and weakly ion-acoustic wave structures to the nonlinear dynamical model via analytical techniques

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

Abstract

This study employs the generalized exponential rational function method and (\(\frac{G^{\prime }}{G^2}\))-expansion function method. Computer algebra is used to study the multiple wave solutions to the (2+1)-dimensional nonlinear Zakharov–Kuznetsov modified equal-width problem. In the study of plasma physics, this model is utilized to represent the effects of a magnetic field on a weak ion-acoustic waves. Bright, dark, singular, and their combo forms solutions are extracted. Besides, the different kinds of the hyperbolic, trigonometric, rational, exponential function and singular periodic wave structures are also obtained. The parameter constraints for the existence of such solitons are also enumerated. With suitable parameter values, the results are shown and supported theoretically by visualizing 3D surface plots, 2D line plots, and corresponding contour graphs. The results of this research show that the methods used to improve the system’s nonlinear dynamical behavior are effective. Intricate phenomena can now be analyzed with computational tools that are not only effective but also easy to use and compatible with one another. We believe that many engineering model professionals will find this work useful as well. Mathematica has been used to confirm the accuracy of these solutions for all retrieved results.

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

Similar content being viewed by others

Data Availability

This study did not use any data.

References

  • Abdelrahman, M.A.E., Sohaly, M.A., Alharbi, A.G.: The new exact solutions for the deterministic and stochastic (2+1)-dimensional equations in natural sciences. J. Taibah Univ. Sci. 13(1), 834–843 (2019)

    Article  Google Scholar 

  • Al-Ghafri, K.S.: Solitary wave solutions of two KdV-type equations. Open Phys. 16(1), 311–318 (2018)

    Article  Google Scholar 

  • Ali, A., Seadawy, A.R., Lu, D.: New solitary wave solutions of some nonlinear models and their applications. Adv. Differ. Equ. 2018(1), 232 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  • Anjum, N., He, J.H.: Laplace transform: making the variational iteration method easier. Appl. Math. Lett. 92, 134–138 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  • Baskonus, H.M., Bulut, H., Atangana, A.: On the complex and hyperbolic structures of the longitudinal wave equation in a magnetoelectro-elastic circular rod. Smart Mater. Struct. 25(3), 035022 (2016)

    Article  ADS  Google Scholar 

  • Bilal, M., Ren, J.: Dynamics of exact solitary wave solutions to the conformable time-space fractional model with reliable analytical approaches. Opt. Quant. Electron. 54, 40 (2022)

    Article  Google Scholar 

  • Bilal, M., Seadawy, A.R., Younis, M., Rizvi, S.T.R., El-Rashidy, K., Mahmoud, S.F.: Analytical wave structures in plasma physics modelled by Gilson–Pickering equation by two integration norms. Results Phys. 23, 103959 (2021a)

  • Bilal, M., Hu, W., Ren, J.: Different wave structures to the Chen–Lee—Liu equation of monomode fibers and its modulation instability analysis. Eur. Phys. J. Plus 136(4), 1–15 (2021b)

    Article  Google Scholar 

  • Bilal, M., Younas, U., Ren, J.: Propagation of diverse solitary wave structures to the dynamical soliton model in mathematical physics. Opt. Quant. Electron. 53, 522 (2021c)

    Article  Google Scholar 

  • Bilal, M., Younas, U., Ren, J.: Dynamics of exact soliton solutions to the coupled nonlinear system with reliable analytical mathematical approaches. Commun. Theor. Phys. 73, 085005 (2021d)

    Article  ADS  MathSciNet  Google Scholar 

  • Bilal, M., Ren, J., Younas, U.: Stability analysis and optical soliton solutions to the nonlinear Schrodinger model with efficient computational techniques. Opt. Quant. Electron. 53, 406 (2021e)

    Article  Google Scholar 

  • Bilal, M., Rehman, S.U., Younas, U., Baskonus, H.M., Younis, M.: Investigation of shallow water waves and solitary waves to the conformable 3D-WBBM model by an analytical method. Phys. Lett. A 403, 127388 (2021f)

    Article  MathSciNet  MATH  Google Scholar 

  • Bilal, M., Younas, U., Ren, J.: Dynamics of exact soliton solutions in the Double-Chain Model of deoxyribonucleic acid. Math. Methods Appl. Sci. 44(17), 13357–13375 (2021g)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Cinar, M., Secer, A., Bayram, M.: Analytical solutions of (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff equation in fluid mechanics/plasma physics using the New Kudryashov method. Phys. Scr. 97(9), 094002 (2022)

    Article  ADS  Google Scholar 

  • Cinar, M., Secer, A., Bayram, M.: On the optical soliton solutions of time-fractional Biswas-Arshed equation including the beta or M-truncated derivatives. Opt. Quant. Electron. 55, 186 (2023)

    Article  Google Scholar 

  • Esen, A., Kutluay, S.: Travelling wave solutions for the generalized (2+1)-dimensional ZK-MEW equation. Int. J. Nonlinear Sci. 8(4), 428–434 (2009)

    MathSciNet  MATH  Google Scholar 

  • Inc, M.: New exact solutions for the ZK-MEW equation by using symbolic computation. Appl. Math. Comput. 189, 508–513 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Kazi Sazzad Hossain, A.K.M., Akbar, M.A.: Closed form solutions of two nonlinear equation via the enhanced \((\frac{G^{\prime }}{G} )\)-expansion method. Cogent Math. 4(1), 1355958 (2017)

  • Malaikah, H.M.: The Adomian decomposition method for solving Volterra–Fredholm integral equation using maple. Appl. Math. 11, 779–787 (2020)

    Article  Google Scholar 

  • Osman, M.S., Baleanu, D., Tariq, K.U., Kaplan, M., Younis, M., Rizvi, S.T.R.: Different types of progressive wave solutions via the 2D-chiral nonlinear Schrödinger equation. Front. Phys. 8, 215 (2020)

    Article  Google Scholar 

  • Ozisik, M., Bayram, M., Secer, A., Yusuf, A., Tukur, T.A.: Optical solitons to the (1+2)-dimensional Chiral non-linear Schrödinger equation. Opt. Quant. Electron. 54, 558 (2022)

    Article  Google Scholar 

  • Seadawy, A.R., Lu, D., Nasreen, N.: Construction of solitary wave solutions of some nonlinear dynamical system arising in nonlinear water wave models. Indian J. Phys. 1–10 (2019a)

  • Seadawy, A.R., Ali, A., Albarakati, W.A.: Analytical wave solutions of the(2+1)-dimensional first integro-differential Kadomtsev Petviashivili hierarchy equation by using modified mathematical methods. Results in Physics 15, 102775 (2019b)

    Article  Google Scholar 

  • Seadawy, A.R., Bilal, M., Younis, M., Rizvi, S.T.R.: Resonant optical solitons with conformable time-fractional nonlinear Schrödinger equation. Int. J. Mod. Phys. B 35(03), 2150044 (2021a)

    Article  ADS  MATH  Google Scholar 

  • Seadawy, A.R., Rehman, S.U., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Modulation instability analysis and longitudinal wave propagation in an elastic cylindrical rod modelled with Pochhammer-Chree equation. Phys. Scr. 96(4), 045202 (2021b)

    Article  ADS  Google Scholar 

  • Shi, D., Zhang, Y.: Diversity of exact solutions to the conformable space-time fractional MEW equation. Appl. Math. Lett. 99, 105994 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, F., Yan, W., Chen, Y.L., Li, C.Q., Zhang, Y.N.: Equation of the two dimensional ZK-MEW equation using Exp-function method. Comput. Math. Appl. 58, 2307–2312 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Yildirim, Y.: Optical solitons of Biswas–Arshed equation by trial equation technique. Optik 182, 876–883 (2019)

    Article  ADS  Google Scholar 

  • Yokus, A.: Construction of different types of traveling wave solutions of the relativistic wave equation associated with the Schrödinger equation. Math. Model. Numer. Simul. Appl. 1(1), 24–31 (2021)

    MathSciNet  Google Scholar 

  • Yokus, A., Baskonus, H.M.: Dynamics of traveling wave solutions arising in fiber optic communication of some nonlinear models. Soft. Comput. (2022). https://doi.org/10.1007/s00500-022-07320-4

    Article  Google Scholar 

  • Younas, U., Seadawy, A.R., Younis, M., Rizvi, S.T.R.: Construction of analytical wave solutions to the conformable fractional dynamical system of ion sound and Langmuir waves. Waves Random Complex Media (2020a)

  • Younas, U., Seadawy, A.R., Younis, M., Rizvi, S.T.R.: Dispersive of propagation wave structures to the Dullin–Gottwald–Holm dynamical equation in a shallow water waves. Chin. J. Phys. 68, 348–364 (2020b)

    Article  MathSciNet  Google Scholar 

  • Younis, M., Cheemaa, N., Mehmood, S.A., Rizvi, S.T.R., Bekir, A.: A variety of exact solutions to (2+ 1)-dimensional schrödinger equation. Waves Random Complex Media 30(3), 490–499 (2020)

    Article  ADS  MathSciNet  MATH  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=Mo, Cu) ternary alloys—a dynamical wave study. Int. J. Mod. Phys. B 2150220 (2021a)

  • Younis, M., Seadawy, A.R., Bilal, M., Rizvi, S.T.R., Althobaiti, S., Alkafafy, M.: Nonlinear dynamical wave structures to the Date-Jimbo–Kashiwara–Miwa equation and its modulation instability analysis. Mod. Phys. Lett. B (2021b)

  • Zayed, E.M.E., Filiz, A., Ekici, M., Sonmezoglu, A., Duran, D.: Exact solutions of the ZK-MEW equation and the Davey–Stewartson equation. Int. J. Appl. Math. Res. 3(2), 122–132 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 52071298), the Strategic Research and Consulting Project of Chinese Academy of Engineering (No. 2022HENYB05), the ZhongYuan Science and Technology Innovation Leadership Program (No. 214200510010).

Author information

Authors and Affiliations

  1. Henan Academy of Big Data/School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

    Muhammad Bilal & Jingli Ren

  2. Department of Mathematics, Science Faculty, Firat University, 23119, Elazig, Turkey

    Mustafa Inc

  3. Department of Medical Research, China Medical University, Taichung, 40402, Taiwan

    Mustafa Inc

  4. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), 11432, Riyadh, Saudi Arabia

    Rubbayi T. Alqahtani

Authors
  1. Muhammad Bilal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jingli Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mustafa Inc
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rubbayi T. Alqahtani
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

MB and RJ wrote the main manuscript text and MI and RTA prepared figures. All authors reviewed the manuscript.

Corresponding author

Correspondence to Mustafa Inc.

Ethics declarations

Conflict of interest

The author declares that they have no conflict of interest.

Ethical approval

The author declares that there is no animal studies in this work.

Consent for publication

All authors have agreed and have given their consent for the publication of this research paper.

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 (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

Bilal, M., Ren, J., Inc, M. et al. Dynamics of solitons and weakly ion-acoustic wave structures to the nonlinear dynamical model via analytical techniques. Opt Quant Electron 55, 656 (2023). https://doi.org/10.1007/s11082-023-04880-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-023-04880-z

Keywords

Search

Navigation