SpringerLink
Log in

New dispersive optical solitons for the (2+1)-dimensional evolution equation in spin dynamics

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

Abstract

In this paper, the investigated new optical soliton solutions are for the \((2+1)\)-dimensional evolution equation which has a potential application in spin dynamics. The new exact solutions of the governing evolution equation namely \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain equation (HFSCE) are achieved by transforming it into the ordinary differential equation and then applying the generalized Kudryashov method which leads to varieties of solutions of hyperbolic, trigonometric, rational types. The resulting solutions show wave patterns of different forms in various conditions including kink, singular-kink, anti-kink and anti-peakon soliton solutions. Furthermore, the characteristics of the obtained wave patterns are depicted and illustrated by graphical representation. Moreover, the dynamics ensured the productivity, efficacy and reliability of the proposed method. Additionally, from the derived solutions the molecular structures, other properties of spin dynamics as well as the properties of optical fibers can be improved by taking necessary approximations to the parameters for a better result.

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

Access this article

Log in via an institution

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 includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data availability statement

On reasonable request, the corresponding author will make accessible the datasets created and/or analysed during the current work.

References

  • AlWoadud, K.M.A., Kumar, D., Islam, M.J., Kayes, M.I., Kundu, A.K.: Extraction of solitary wave features to the Heisenberg ferromagnetic spin chain and the complex Klein–Gordon equations. Int. J. Appl. Comput. Math. 5(3), 1–11 (2019)

    MathSciNet  MATH  Google Scholar 

  • Ali, I., Rizvi, S.T.R., Abbas, S.O., Zhou, Q.: Optical solitons for modulated compressional dispersive Alfven and Heisenberg ferromagnetic spin chains. Results Phys. 15, 102714 (2019)

    Google Scholar 

  • Ali, F., Jhangeer, A., Muddassar, M., Almusawa, H.: Solitonic, quasi-periodic, super nonlinear and chaotic behaviors of a dispersive extended nonlinear Schrödinger equation in an optical fiber. Results Phys. 31, 104921 (2021)

    Google Scholar 

  • Anitha, T., Latha, M.M., Vasanthi, C.C.: Dromions in \((2+1)\)-dimensional ferromagnetic spin chain with bilinear and biquadratic interactions. Physica A 415, 105–115 (2014)

    ADS  MathSciNet  MATH  Google Scholar 

  • Bashar, M.H., Islam, S.M.R.: Exact solutions to the \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain equation by using modified simple equation and improve F-expansion methods. Physics Open 5, 100027 (2020)

    Google Scholar 

  • Du, X.X., Tian, B., Yuan, Y.Q., Du, Z.: Symmetry reductions, group-invariant solutions, and conservation laws of a \((2+1)\)-dimensional nonlinear Schrödinger equation in a Heisenberg ferromagnetic spin chain. Ann. Phys. 531(11), 1–11 (2019)

    Google Scholar 

  • Guan, B., Chen, S., Liu, Y., Wang, X., Zhao, J.: Wave patterns of \((2+1)\)-dimensional nonlinear Heisenberg ferromagnetic spin chains in the semiclassical limit. Results Phys. 16, 102834 (2020)

    Google Scholar 

  • Guo, D., Tian, S.F., Zhang, T.T.: Integrability, soliton solutions and modulation instability analysis of a \((2+1)\)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation. Comput. Math. Appl. 77(3), 770–778 (2019)

    MathSciNet  MATH  Google Scholar 

  • Hashemi, M.S.: Some new exact solutions of \((2+1)\)-dimensional nonlinear Heisenberg ferromagnetic spin chain with the conformable time fractional derivative. Opt. Quantum Electron. 50(2), 1–11 (2018)

    MathSciNet  Google Scholar 

  • Hosseini, K., Matinfar, M., Mirzazadeh, M.: Soliton solutions of high-order nonlinear Schrödinger equations with different laws of nonlinearities. Regul. Chaot. Dyn. 26(1), 105–112 (2021)

    ADS  MATH  Google Scholar 

  • Hosseini, K., Salahshour, S., Mirzazadeh, M., Ahmadian, A., Baleanu, D., Khoshrang, A.: The \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions. Eur. Phys. J. Plus 136(2), 1–9 (2021)

    Google Scholar 

  • Hosseini, K., Kaur, L., Mirzazadeh, M., Baskonus, H.M.: 1-soliton solutions of the \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain model with the beta time derivative. Opt. Quantum Electron. 53(2), 1–10 (2021)

    Google Scholar 

  • Inc, M., Aliyu, A.I., Yusuf, A., Baleanu, D.: Optical solitons and modulation instability analysis of an integrable model of \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain equation. Superlattices Microstruct. 112, 628–638 (2017)

    ADS  Google Scholar 

  • Islam, M.S., Khan, K., Arnous, A.H.: Generalized Kudryashov method for solving some \((3+1)\)-dimensional nonlinear evolution equations. New Trends Math. Sci. 57(3), 46–57 (2015)

    MathSciNet  Google Scholar 

  • Jhangeer, A., Raza, N., Rezazadeh, H., Seadawy, A.R.: Nonlinear self-adjointness, conserved quantities, bifurcation analysis and travelling wave solutions of a family of long-wave unstable lubrication model. Pramana 94(1), 1–9 (2020)

    Google Scholar 

  • Jhangeer, A., Faridi, W.A., Asjad, M.I., Akgül, A.: Analytical study of soliton solutions for an improved perturbed Schrödinger equation with Kerr law non-linearity in non-linear optics by an expansion algorithm. Part. Differ. Equ. Appl. Math. 4, 100102 (2021)

    Google Scholar 

  • Jhangeer, A., Baskonus, H.M., Yel, G., Gao, W.: New exact solitary wave solutions, bifurcation analysis and first order conserved quantities of resonance nonlinear Schrödinger’s equation with Kerr law nonlinearity. J. King Saud Univer.-Sci. 33(1), 101180 (2021)

    Google Scholar 

  • Jhangeer, A., Rezazadeh, H., Seadawy, A.R.: A study of travelling, periodic, quasiperiodic and chaotic structures of perturbed Fokas–Lenells model. Pramana 95(1), 1–11 (2021)

    ADS  Google Scholar 

  • Jhangeer, A., Hussain, A., Junaid-U-Rehman, M., Baleanu, D., Riaz, M.B.: Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation. Chaos, Solitons Fractals 143, 110578 (2021)

    MathSciNet  MATH  Google Scholar 

  • Jhangeer, A., Muddassar, M., Awrejcewicz, J., Naz, Z., Riaz, M.B.: Phase portrait, multi-stability, sensitivity and chaotic analysis of Gardner’s equation with their wave turbulence and solitons solutions. Results Phys. 32, 104981 (2022)

  • Khater, M.M.A., Jhangeer, A., Rezazadeh, H., Akinyemi, L., Akbar, M.A., Inc, M.: Propagation of new dynamics of longitudinal bud equation among a magneto-electro-elastic round rod. Mod. Phys. Lett. B 35(35), 2150381 (2021)

    ADS  MathSciNet  Google Scholar 

  • Kudryashov, N.A.: One method for finding exact solutions of nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simul. 17(6), 2248–2253 (2012)

    ADS  MathSciNet  MATH  Google Scholar 

  • Lan, Z., Gao, B.: Lax pair, infinitely many conservation laws and solitons for a \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain equation with time-dependent coefficients. Appl. Math. Lett. 79, 6–12 (2018)

    MathSciNet  MATH  Google Scholar 

  • Latha, M.M., Vasanthi, C.C.: An integrable model of \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain and soliton excitations. Phys. Scr. 89(6), 065204 (2014)

    ADS  Google Scholar 

  • Li, B.Q., Ma, Y.L.: Lax pair, Darboux transformation and Nth-order rogue wave solutions for a \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain equation. Comput. Math. Appl. 77(2), 514–524 (2019)

    MathSciNet  MATH  Google Scholar 

  • Ma, Y.L., Li, B.Q., Fu, Y.Y.: A series of the solutions for the Heisenberg ferromagnetic spin chain equation. Math. Methods Appl. Sci. 41(9), 3316–3322 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  • Osman, M.S., Tariq, K.U., Bekir, A., Elmoasry, A., Elazab, N.S., Younis, M., Abdel-Aty, M.: Investigation of soliton solutions with different wave structures to the \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain equation. Commun. Theor. Phys. 72(3), 035002 (2020)

    ADS  MathSciNet  MATH  Google Scholar 

  • Peng, L.J.: Nonautonomous complex wave solutions for the \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain equation with variable coefficients. Opt. Quantum Electron. 51(6), 1–10 (2019)

    Google Scholar 

  • Raza, N., Seadawy, A.R., Jhangeer, A., Butt, A.R., Arshed, S.: Dynamical behavior of micro-structured solids with conformable time fractional strain wave equation. Phys. Lett. A 384(27), 126683 (2020)

    MathSciNet  MATH  Google Scholar 

  • Riaz, M.B., Awrejcewicz, J., Jhangeer, A., Junaid-U-Rehman, M.: A variety of new traveling wave packets and conservation laws to the nonlinear low-pass electrical transmission lines via lie analysis. Fractal Fract. 5(4), 170 (2021)

    Google Scholar 

  • Sahoo, S., Ray, S.S., Abdou, M.A.: New exact solutions for time-fractional Kaup–Kupershmidt equation using improved \(\left(\dfrac{G^{\prime }}{G}\right)\)-expansion and extended \(\left(\dfrac{G^{\prime }}{G}\right)\)-expansion methods. Alex. Eng. J. 59(5), 3105–3110 (2020)

    Google Scholar 

  • Sahoo, S., Ray, S.S., Abdou, M.A.M., Inc, M., Chu, Y.M.: New soliton solutions of fractional Jaulent–Miodek system with symmetry analysis. Symmetry 12(6), 1–14 (2020)

    Google Scholar 

  • Sulaiman, T.A., Aktürk, T., Bulut, H., Baskonus, H.M.: Investigation of various soliton solutions to the Heisenberg ferromagnetic spin chain equation. J. Electromagn. Waves Appl. 32(9), 1093–1105 (2018)

    Google Scholar 

  • Sulaiman, T.A., Nuruddeen, R.I., Mikail, B.B.: Dark and singular solitons to the two nonlinear Schrödinger equations. Optik 186, 423–430 (2019)

    ADS  Google Scholar 

  • Tahir, M., Kumar, S., Rehman, H., Ramzan, M., Hasan, A., Osman, M.S.: Exact traveling wave solutions of Chaffee–Infante equation in \((2+1)\)-dimensions and dimensionless Zakharov equation. Math. Methods Appl. Sci. 44(2), 1500–1513 (2021)

    ADS  MathSciNet  MATH  Google Scholar 

  • Triki, H., Wazwaz, A.M.: New solitons and periodic wave solutions for the \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain equation. J. Electromagn. Waves Appl. 30(6), 788–794 (2016)

    Google Scholar 

  • Tripathy, A., Sahoo, S.: Exact solutions for the ion sound Langmuir wave model by using two novel analytical methods. Results Phys. 19, 103494 (2020)

    Google Scholar 

  • Wazwaz, A.M.: A \((2+1)\)-dimensional time-dependent Date–Jimbo–Kashiwara–Miwa equation: Painlevé integrability and multiple soliton solutions. Comput. Math. Appl. 79(4), 1145–1149 (2019)

    MATH  Google Scholar 

  • Wazwaz, A.M.: Painlevé analysis for Boiti–Leon–Manna–Pempinelli equation of higher dimensions with time-dependent coefficients: multiple soliton solutions. Phys. Lett. A 384(16), 126310 (2020)

    MathSciNet  MATH  Google Scholar 

  • Zhao, X.H., Tian, B., Liu, D.Y., Wu, X.Y., Chai, J., Guo, Y.J.: Dark solitons interaction for a \((2+1)\)-dimensional nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain. Superlattices Microstruct. 100, 587–595 (2016)

    ADS  Google Scholar 

  • Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M., Eslami, M.: Analytical study of solitons to Biswas–Milovic model in nonlinear optics. J. Mod. Opt. 63(21), 2131–2137 (2016)

    ADS  Google Scholar 

Download references

Funding

There is no financial assistance or funding for the development of this manuscript.

Author information

Authors and Affiliations

  1. Kalinga Institute of Industrial Technology, Deemed to be University, Bhubaneswar, Odisha, 751024, India

    A. Tripathy & S. Sahoo

Authors
  1. A. Tripathy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Sahoo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Sahoo.

Ethics declarations

Conflict of interest

The authors declare that they have no 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

Tripathy, A., Sahoo, S. New dispersive optical solitons for the (2+1)-dimensional evolution equation in spin dynamics. Opt Quant Electron 54, 598 (2022). https://doi.org/10.1007/s11082-022-04032-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-022-04032-9

Keywords

Mathematics Subject Classification

Search

Navigation