Skip to main content
SpringerLink
Log in

New interaction and combined multi-wave solutions for the Heisenberg ferromagnetic spin chain equation

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

In the current study, rational, interaction and combined multi-wave solutions are obtained for Heisenberg ferromagnetic spin chain equation by using the logarithmic transformation and symbolic computation with ansatz functions. By the choice of suitable parameter values, the dynamics of these obtained solutions are analyzed and represented in figures. The dynamics and characteristics of lump–kink, soliton and multi-wave interactions observed through graphical analysis.

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

Similar content being viewed by others

References

  1. C. Kharif, E. Pelinovsky, A. Slunyaey, Rogue Waves in the Ocean, Observation,Theories and Modeling (Springer, New York, 2009)

    Google Scholar 

  2. D.H. Peregrine, Water waves, nonlinear Schrodinger equations and their solutions. J. Aust. Math. Soc. Ser. B Appl. Math. 25, 1643 (1983)

    Article  MathSciNet  Google Scholar 

  3. N. Akhmediev, A. Ankiewicz, J.M. Soto-Crespo, Rogue waves and rational solutions of the nonlinear Schrodinger equation. Phys. Rev. E 80, 026601 (2009)

    Article  ADS  Google Scholar 

  4. D.R. Solli, C. Ropers, P. Koonath, B. Jalali, Optical rogue waves. Nature 450, 1054–1057 (2007)

    Article  ADS  Google Scholar 

  5. A. Montina, U. Bortolozzo, S. Residori, F.T. Arecchi, Rogue waves and their generating mechanisms in different physical contexts. Phys. Rep. 528, 47–89 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  6. V.E. Zakharov, Exact solutions in the problem of parametric interaction of three-dimensional wave packets. Dokl. Acad. Nauk SSSR 228(6), 1314–1316 (1976)

    ADS  MathSciNet  Google Scholar 

  7. A.D.D. Craik, J.A. Adam, Evolution in space and time of resonant wave triads-I. The pump-wave approximation. Proc. R. Soc. A 363, 243–255 (1978)

    ADS  MathSciNet  MATH  Google Scholar 

  8. W.X. Ma, Lump solutions to the Kadomtsev–Petviashvili equation. Phys. Lett. A 379, 1975–1978 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  9. J.Y. Yang, W.X. Ma, Lump solutions to the BKP equation by symbolic computation. Int. J. Mod. Phys. B 30, 1640028 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  10. W.X. Ma, Z.Y. Qin, X. Lv, Lump solutions to dimensionally reduced pgKP and pgbKP equations. Nonlinear Dyn. 84, 923–931 (2016)

    Article  Google Scholar 

  11. C.J. Wang, Spatiotemporal deformation of lump solution to (2+1)-dimensional KdV equation. Nonlinear Dyn. 84, 697–702 (2016)

    Article  MathSciNet  Google Scholar 

  12. C.J. Wang, Z.D. Dai, C.F. Liu, Interaction between kink solitary wave and Rogue wave for (2+1)-dimensional Burgers equation. Mediterr. J. Math. 13, 1087–1098 (2016)

    Article  MathSciNet  Google Scholar 

  13. S. Ali, M. Younis, Rogue wave solutions and modulation instability with variable coefficient and harmonica potential. Front. Phys. (2019). https://doi.org/10.3389/fphy.2019.00255

    Article  Google Scholar 

  14. B. Younas, M. Younis, Chirped solitons in optical monomode fibres modelled with Chen–Lee–Liu equation. Pramana 94(1), 3 (2020)

    Article  ADS  Google Scholar 

  15. A. Arif, M. Younis, M. Imran, M. Tantawy, S.T.R. Rizvi, Solitons and lump wave solutions to the graphene thermophoretic motion system with a variable heat transmission. Eur. Phys. J. Plus 134(6), 303 (2019)

    Article  Google Scholar 

  16. S.T.R. Rizvi, I. Afzal, K. Ali, M. Younis, Stationary solutions for nonlinear Schrödinger equations by Lie group analysis. Acta Phys. Pol. A 136, 187–189 (2019)

    Article  ADS  Google Scholar 

  17. S. Ali, M. Younis, M.O. Ahmad, S.T.R. Rizvi, Rogue wave solutions in nonlinear optics with coupled Schrodinger equations. Opt. Quantum Electron. 50(7), 266 (2018)

    Article  Google Scholar 

  18. X. Lu, W.X. Ma, Y. Zhou, C.M. Khalique, Rational solutions to an extended Kadomtsev–Petviashvili-like equation with symbolic computation. Comput. Math. Appl. 71, 1560–1567 (2016)

    Article  MathSciNet  Google Scholar 

  19. X. Lu, W.X. Ma, S.T. Chen, C.M. Khalique, A note on rational solutions to a Hirota–Satsuma-like equation. Appl. Math. Lett. 58, 13–18 (2016)

    Article  MathSciNet  Google Scholar 

  20. F.H. Lin, S.T. Chen, Q.X. Qu, J.P. Wang, X.W. Zhou, X. Lu, Resonant multiple wave solutions to a new (3+1)-dimensional generalized Kadomtsev–Petviashvili equation: linear superposition principle. Appl. Math. Lett. 78, 112–117 (2018)

    Article  MathSciNet  Google Scholar 

  21. X. Lu, J.P. Wang, F.H. Lin, X.W. Zhou, Lump dynamics of a generalized two-dimensional Boussinesq equation in shallow water. Nonlinear Dyn. 91, 1249–1259 (2018)

    Article  Google Scholar 

  22. X. Lu, S.T. Chen, W.X. Ma, Constructing lump solutions to a generalized Kadomtsev–Petviashvili–Boussinesq equation. Nonlinear Dyn. 86, 523–534 (2016)

    Article  MathSciNet  Google Scholar 

  23. S.J. Chen, Y.H. Yin, W.X. Ma, Abundant exact solutions and interaction phenomena of the (2 + 1)-dimensional YTSF equation. Anal. Math. Phys. 9, 2329–2344 (2019)

    Article  MathSciNet  Google Scholar 

  24. W.X. Ma, Interaction solutions to Hirota–Satsuma–Ito equation in (2 + 1)-dimensions. Front. Math. China 14, 619–629 (2019)

    Article  MathSciNet  Google Scholar 

  25. W.X. Ma, Lump and interaction solutions to linear PDEs in 2+1 dimensions via symbolic computation. Mod. Phys. Lett. B 33, 1950457 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  26. W.X. Ma, L. Zhang, Lump solutions with higher-order rational dispersion relations. Pramana J. Phys. 94, 43 (2020)

    Article  ADS  Google Scholar 

  27. W.X. Ma, Long-time asymptotics of a three-component coupled mKdV system. Mathematics 7, 573 (2019)

    Article  Google Scholar 

  28. W.X. Ma, Inverse scattering for nonlocal reverse-time nonlinear Schrödinger equations. Appl. Math. Lett. 102, 106161 (2020)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  30. M. Daniel, L. Kavitha, R. Amuda, Soliton spin excitations in an anisotropic Heisenberg ferromagnet with octupole–dipole interaction. Phys. Rev. 59, 13774 (1999)

    Article  Google Scholar 

  31. M. Daniel, Magnetization reversal through soliton flip in a biquadratic ferromagnet with varying exchange interactions. Phys. Rev. 66, 184433 (2002)

    Article  Google Scholar 

  32. M. Daniel, V. Veerakumar, R. Amuda, Soliton and electromagnetic wave propagation in a ferromagnetic medium. Phys. Rev. 55, 3619 (1997)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering Istanbul, Biruni University, Istanbul, Turkey

    Abdullahi Yusuf

  2. Department of Mathematics Jigawa, Faculty of Science, Federal University, Dutse, Dutse, Nigeria

    Abdullahi Yusuf

  3. Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh, 11495, Saudi Arabia

    Fairouz Tchier

  4. Department of Mathematics, Faculty of Science, Firat University, Elazig, Turkey

    Mustafa Inc

  5. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Mustafa Inc

Authors
  1. Abdullahi Yusuf
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fairouz Tchier
    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

Corresponding author

Correspondence to Mustafa Inc.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yusuf, A., Tchier, F. & Inc, M. New interaction and combined multi-wave solutions for the Heisenberg ferromagnetic spin chain equation. Eur. Phys. J. Plus 135, 416 (2020). https://doi.org/10.1140/epjp/s13360-020-00425-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-020-00425-5

Search

Navigation