Log in

Stability and solitonic wave solutions of (2+1)-dimensional chiral nonlinear Schrödinger equation

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

Abstract

In this work, the (2+1)-dimensional chiral nonlinear Schrödinger equation that describes about quantum field concept in physics and other physical sciences are studied and solved by utilizing the two modern techniques including the polynomial expansion method and the Sardar sub-equation method. We attained different types of soliton solutions that had been applications in different fields of mathematical sciences. The behaviours of attained solutions are periodic, singular and v-shaped soliton solutions. Furthermore, we have investigated the stability of the obtained results. Also, the 3D, 2D, and contour graphics are displayed for the better understanding of the dynamical behaviour of various waves structures extensively. The techniques applied in this article are not used in this model in literature so we say that our findings are new that summarize the novelty of work. The utilize model has applications in physics related phenomenon also obtained results highly valuable in various branches of sciences specially in the transmission of fiber optical.

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
Fig. 7

Similar content being viewed by others

Availability of data and materials

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

References

  • Abdelwahed, H., Alsarhan, A., El-Shewy, E., Abdelrahman, M.A., et al.: Novel explosive and super fractional nonlinear schrödinger structures. J. Math. (2023)

  • Abdelwahed, H., Alsarhana, A., El-Shewy, E., Abdelrahman, M.A.: Characteristics of new stochastic solitonic solutions for the chiral type of nonlinear schrödinger equation. Fractal Fractional 7(6), 461 (2023)

    Article  Google Scholar 

  • Ahmad, S., Saifullah, S., Khan, A., Inc, M.: New local and nonlocal soliton solutions of a nonlocal reverse space-time mkdv equation using improved hirota bilinear method. Phys. Lett. A 450, 128393 (2022)

    Article  MathSciNet  Google Scholar 

  • Ahmad, J., Mustafa, Z., Turki, N.B., Shah, N.A., et al.: Solitary wave structures for the stochastic nizhnik-novikov-veselov system via modified generalized rational exponential function method. Res. Phys. 52, 106776 (2023)

    Google Scholar 

  • Ahmad, J., Noor, K., Anwar, S., Akram, S.: Stability analysis and soliton solutions of truncated m-fractional heisenberg ferromagnetic spin chain model via two analytical methods. Opt. Quant. Electronics 56(1), 95 (2024)

    Article  ADS  Google Scholar 

  • Akinyemi, L., Inc, M., Khater, M.M., Rezazadeh, H.: Dynamical behaviour of Chiral nonlinear Schrödinger equation. Opt. Quant. Electronics 54(3), 191 (2022)

    Article  Google Scholar 

  • Akram, S., Ahmad, J., Alkarni, S., Shah, N.A., et al.: Analysis of lump solutions and modulation instability to fractional complex ginzburg-landau equation arise in optical fibers. Res. Phys. 53, 106991 (2023)

    Google Scholar 

  • Akram, S., Ahmad, J., Sarwar, S., Ali, A.: Dynamics of soliton solutions in optical fibers modelled by perturbed nonlinear schrödinger equation and stability analysis. Opt. Quant. Electronics 55(5), 450 (2023)

    Article  Google Scholar 

  • Almatrafi, M., Alharbi, A.: New soliton wave solutions to a nonlinear equation arising in plasma physics., CMES Comput. Model. Eng. Sci. 137(1)

  • Almuneef, A., Alqahtani, Z., El-Shewy, E., Abdelrahman, M.A.: Simulation of new waves in applied sciences via schrödinger equations. J. Taibah Univ. Sci. 18(1), 2285082 (2024)

    Article  Google Scholar 

  • Arnous, A.H., Hashemi, M.S., Nisar, K.S., Shakeel, M., Ahmad, J., Ahmad, I., Jan, R., Ali, A., Kapoor, M., Shah, N.A.: Investigating solitary wave solutions with enhanced algebraic method for new extended sakovich equations in fluid dynamics. Res. Phys. 57, 107369 (2024)

    Google Scholar 

  • Arora, G., Rani, R., Emadifar, H.: Numerical solutions of nonlinear schrodinger equation with applications in optical fiber communication. Optik 266, 169661 (2022)

    Article  ADS  Google Scholar 

  • Arshad, M., Seadawy, A.R., Lu, D.: Bright-dark solitary wave solutions of generalized higher-order nonlinear schrödinger equation and its applications in optics. J. Electromagnetic Waves Appl. 31(16), 1711–1721 (2017)

    Article  ADS  Google Scholar 

  • Arshad, M., Seadawy, A.R., Lu, D.: Study of soliton solutions of higher-order nonlinear schrödinger dynamical model with derivative non-kerr nonlinear terms and modulation instability analysis. Res. Phys. 13, 102305 (2019)

    Google Scholar 

  • Belyaev, A., Dunster, J.L., Gibbins, J.M., Panteleev, M.A., Volpert, V.: Modeling thrombosis in silico: frontiers, challenges, unresolved problems and milestones. Phys. Life Rev. 26, 57–95 (2018)

    Article  ADS  Google Scholar 

  • El-Rashidy, K.: New traveling wave solutions for the higher Sharma–Tasso–Olver equation by using extension exponential rational function method. Res. Phys. 17, 103066 (2020)

    Google Scholar 

  • Hosseini, K., Mirzazadeh, M., Osman, M., Al Qurashi, M., Baleanu, D.: Solitons and jacobi elliptic function solutions to the complex Ginzburg–Landau equation. Front. Phys. 8, 225 (2020)

    Article  Google Scholar 

  • Huang, W.-H.: A polynomial expansion method and its application in the coupled Zakharov–Kuznetsov equations. Chaos Solitons Fractals 29(2), 365–371 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  • Islam, N., Khan, K., Islam, M.H.: Travelling wave solution of Dodd–Bullough–Mikhailov equation: a comparative study between generalized kudryashov and improved f-expansion methods. J. Phys. Commun. 3(5), 055004 (2019)

    Article  Google Scholar 

  • Islam, M.T., Akbar, M.A., Ahmad, H., Ilhan, O.A., Gepreel, K.A.: Diverse and novel soliton structures of coupled nonlinear schrödinger type equations through two competent techniques. Mod. Phys. Lett. B 36(11), 2250004 (2022)

    Article  ADS  Google Scholar 

  • Islam, M.T., Sarkar, T.R., Abdullah, F.A., Gómez-Aguilar, J.: Distinct optical soliton solutions to the fractional hirota maccari system through two separate strategies. Optik 300, 171656 (2024)

    Article  ADS  Google Scholar 

  • Javeed, S., Abbasi, M.A., Imran, T., Fayyaz, R., Ahmad, H., Botmart, T.: New soliton solutions of simplified modified camassa holm equation, Klein–Gordon–Zakharov equation using first integral method and exponential function method. Res. Phys. 38, 105506 (2022)

    Google Scholar 

  • Karjanto, N.: The nonlinear schrödinger equation: A mathematical model with its wide-ranging applications, ar**v preprint ar**v:1912.10683

  • Khater, M., Anwar, S., Tariq, K.U., Mohamed, M.S.: Some optical soliton solutions to the perturbed nonlinear schrödinger equation by modified khater method. AIP Adv. 11(2)

  • Korkmaz, A., Hepson, O.E., Hosseini, K., Rezazadeh, H., Eslami, M.: Sine-gordon expansion method for exact solutions to conformable time fractional equations in rlw-class. J. King Saud Univ. Sci. 32(1), 567–574 (2020)

    Article  Google Scholar 

  • Mohammed, W.W., Albalahi, A., Albadrani, S., Aly, E., Sidaoui, R., Matouk, A.: The analytical solutions of the stochastic fractional kuramoto-sivashinsky equation by using the Riccati equation method. Math. Prob. Eng. 2022, 1–8 (2022)

    Google Scholar 

  • Peng, X., Zhao, Y.-W., Lü, X.: Data-driven solitons and parameter discovery to the (2+ 1)-dimensional nlse in optical fiber communications. Nonlinear Dyn., pp. 1–16 (2023)

  • Rehman, S.-U., Bilal, M., Ahmad, J.: Highly dispersive optical and other soliton solutions to fiber bragg gratings with the application of different mechanisms. Int. J. Mod. Phys. B 36(28), 2250193 (2022)

    Article  ADS  Google Scholar 

  • Rehman, H.U., Akber, R., Wazwaz, A.-M., Alshehri, H.M., Osman, M.: Analysis of Brownian motion in stochastic Schrödinger wave equation using sardar sub-equation method. Optik 289, 171305 (2023)

    Article  ADS  Google Scholar 

  • Tariq, K.U., Wazwaz, A., Kazmi, S.R.: On the dynamics of the (2+ 1)-dimensional chiral nonlinear Schrödinger model in physics. Optik 285, 170943 (2023)

    Article  ADS  Google Scholar 

  • Ur Rehman, S., Ahmad, J.: Stability analysis and novel optical pulses to Kundu–Mukherjee–Naskar model in birefringent fibers. Int. J. Mod. Phys. B 2450192 (2023)

  • Ur Rehman, H., Asjad Imran, M., Bibi, M., Riaz, M., Akgül, A.: New soliton solutions of the 2d-chiral nonlinear Schrodinger equation using two integration schemes. Math. Methods Appl. Sci. 44(7), 5663–5682 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  • Wang, J., Krstic, M.: Delay-compensated event-triggered boundary control of hyperbolic pdes for deep-sea construction. Automatica 138, 110137 (2022)

    Article  MathSciNet  Google Scholar 

  • Yang, X.-J., Kumar, D., et al.: New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics. Frontiers Media SA, Lausanne (2023)

    Google Scholar 

  • Younas, U., Sulaiman, T.A., Ren, J.: On the study of optical soliton solutions to the three-component coupled nonlinear schrödinger equation: applications in fiber optics. Opt. Quant. Electronics 55(1), 72 (2023)

    Article  Google Scholar 

  • Zafar, A., Ali, K.K., Raheel, M., Nisar, K.S., Bekir, A.: Abundant m-fractional optical solitons to the pertubed Gerdjikov–Ivanov equation treating the mathematical nonlinear optics. Opt. Quant. Electronics 54(1), 25 (2022)

    Article  Google Scholar 

  • Zayed, E.M., Gepreel, K.A., Shohib, R.M., Alngar, M.E., Yıldırım, Y.: Optical solitons for the perturbed Biswas–Milovic equation with Kudryashov’s law of refractive index by the unified auxiliary equation method. Optik 230, 166286 (2021)

    Article  ADS  Google Scholar 

Download references

Funding

Not available.

Author information

Authors and Affiliations

Authors

Contributions

XZ and KUT supervised the project, handled administration, developed methodology, conceptualized, and validated. HR was responsible for identifying the research problem, analyzing outcomes, and reviewing and editing. SMRK conducted formal analysis and investigation, wrote the original draft. MAH handled visualization, analyzed the outcomes, and participated in the review and editing process.

Corresponding authors

Correspondence to Kalim U. Tariq or Hadi Rezazadeh.

Ethics declarations

Conflict of interest

The authors declare no Conflict of interest.

Ethics approval

Not applicable.

Consent for publication

All the authors have agreed and 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

Zhou, X., Tariq, K.U., Rezazadeh, H. et al. Stability and solitonic wave solutions of (2+1)-dimensional chiral nonlinear Schrödinger equation. Opt Quant Electron 56, 1228 (2024). https://doi.org/10.1007/s11082-024-06920-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-024-06920-8

Keywords

Navigation