Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

N-fold Darboux transformation and solitonic interactions for the Kraenkel–Manna–Merle system in a saturated ferromagnetic material

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Ferromagnetic-material investigations are active, with the applications in direct-current power supplies, radios, televisions, high-frequency power supplies, microwave equipments, magnetic recorders, electrodes, sensors, ferrofluids, etc. In this paper, we investigate the Kraenkel–Manna–Merle system for the ultra-short waves in a saturated ferromagnetic material with the zero conductivity in the presence of an external field. N-fold Darboux transformation of that system is derived via an existing Lax pair, where N is a positive integer. Three- and four-fold solutions of that system are determined via \(N=3\) and \(N=4\) in our N-fold Darboux transformation. With respect to the magnetization and external magnetic field related to the saturated ferromagnetic material, interaction among the three solitons and interaction among the four solitons are graphically depicted, which may be useful in understanding certain nonlinear phenomena in the ferromagnetic materials.

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
$34.99 /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.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Data availability

This paper has no associated data.

References

  1. Vedmedenko, E.Y., Kawakami, R.K., Sheka, D.D., Gambardella, P., Kirilyuk, A., Hirohata, A., Binek, C., Chubykalo-Fesenko, O., Sanvito, S., Kirby, B.J., Grollier, J., Everschor-Sitte, K., Kampfrath, T., You, C.Y., Berger, A.: The 2020 magnetism roadmap. J. Phys. D: Appl. Phys. 53, 453001 (2020)

    Google Scholar 

  2. Barman, A., Sinha, J.: Spin Dynamics and Damping in Ferromagnetic Thin Films and Nanostructures. Springer, Cham (2018)

    Google Scholar 

  3. Goldman, A.: Modern Ferrite Technology. Springer, New York (1993)

    Google Scholar 

  4. Shi, P.: One-dimensional magneto-mechanical model for an hysteretic magnetization and magnetostriction in ferromagnetic materials. J. Magn. Magn. Mater. 537, 168212 (2021)

    Google Scholar 

  5. Davidson, A., Amin, V.P., Aljuaid, W.S., Haney, P.M., Fan, X.: Perspectives of electrically generated spin currents in ferromagnetic materials. Phys. Lett. A 384, 126228 (2020)

    Google Scholar 

  6. Walter, J., Voigt, B., Day-Roberts, E., Heltemes, K., Fernandes, R.M., Birol, T., Leighton, C.: Voltage-induced ferromagnetism in a diamagnet. Sci. Adv. 6, eabb7721 (2020)

  7. Nevirkovets, I.P., Mukhanov, O.A.: Memory cell for high-density arrays based on a multiterminal superconducting-ferromagnetic device. Phys. Rev. Appl. 10, 034013 (2018)

    Google Scholar 

  8. Ermolaev, A.V., Sheveleva, A., Genty, G., Finot, C., Dudley, J.M.: Data-driven model discovery of ideal four-wave mixing in nonlinear fibre optics. Sci. Rep. 12, 12711 (2022)

    Google Scholar 

  9. Wazwaz, A.M.: Integrable (3+1)-dimensional Ito equation: variety of lump solutions and multiple-soliton solutions. Nonlinear Dyn. 109, 1929 (2022)

    Google Scholar 

  10. Katsimiga, G.C., Mistakidis, S.I., Schmelcher, P., Kevrekidis, P.G.: Phase diagram, stability and magnetic properties of nonlinear excitations in spinor Bose-Einstein condensates. New J. Phys. 23, 013015 (2021)

    MathSciNet  Google Scholar 

  11. Kumar, S., Mohan, B., Kumar, R.: Lump, soliton, and interaction solutions to a generalized two-mode higher-order nonlinear evolution equation in plasma physics. Nonlinear Dyn. 110, 693 (2022)

    Google Scholar 

  12. Lakshmanan, M., Porsezian, K., Daniel, M.: Effect of discreteness on the continuum limit of the Heisenberg spin chain. Phys. Lett. A 133, 483 (1988)

    Google Scholar 

  13. Sun, W.R.: Vector solitons and rogue waves of the matrix Lakshmanan-Porsezian-Daniel equation. Nonlinear Dyn. 102, 1743 (2020)

    Google Scholar 

  14. Deng, Z.H., Wu, T., Tang, B., Wang, X.Y., Zhao, H.P., Deng, K.: Breathers and rogue waves in a ferromagnetic thin film with the Dzyaloshinskii-Moriya interaction. Eur. Phys. J. Plus 133, 450 (2018)

    Google Scholar 

  15. Gao, X.Y., Guo, Y.J., Shan, W.R., Yin, H.M., Du, X.X., Yang, D.Y.: Certain electromagnetic waves in a ferromagnetic film. Commun. Nonlinear Sci. Numer. Simul. 105, 106066 (2022)

    MathSciNet  MATH  Google Scholar 

  16. Kraenkel, R.A., Manna, M.A., Merle, V.: Nonlinear short-wave propagation in ferrites. Phys. Rev. E 61, 976 (2000)

    Google Scholar 

  17. Nguepjouo, F.T., Kuetche, V.K., Kofane, T.C.: Soliton interactions between multivalued localized waveguide channels within ferrites. Phys. Rev. E 89, 063201 (2014)

    Google Scholar 

  18. Tchokouansi, H.T., Kuetche, V.K., Kofane, T.C.: On the propagation of solitons in ferrites: the inverse scattering approach. Chaos Solitons Fract. 86, 64 (2016)

    MathSciNet  MATH  Google Scholar 

  19. Ma, Y.L., Li, B.Q.: Kraenkel-Manna-Merle saturated ferromagnetic system: Darboux transformation and loop-like soliton excitations. Chaos Solitons Fract. 159, 112179 (2022)

    MathSciNet  Google Scholar 

  20. Jin, X.W., Lin, J.: Rogue wave, interaction solutions to the KMM system. J. Magn. Magn. Mater. 502, 166590 (2020)

    Google Scholar 

  21. Li, B.Q., Ma, Y.L.: Oscillation rogue waves for the Kraenkel-Manna-Merle system in ferrites. J. Magn. Magn. Mater. 537, 168182 (2021)

    Google Scholar 

  22. Li, B.Q., Ma, Y.L.: Rich soliton structures for the Kraenkel-Manna-Merle (KMM) system in ferromagnetic materials. J. Supercond. Nov. Magn. 31, 1773 (2018)

    Google Scholar 

  23. Younas, U., Sulaiman, T.A., Yusuf, A., Bilal, M., Younis, M., Rehman, S.U.: New solitons and other solutions in saturated ferromagnetic materials modeled by Kraenkel-Manna-Merle system. Indian J. Phys. 96, 181 (2021)

    Google Scholar 

  24. Rehman, S.U., Bilal, M., Ahmad, J.: Dynamics of soliton solutions in saturated ferromagnetic materials by a novel mathematical method. J. Magn. Magn. Mater. 538, 168245 (2021)

    Google Scholar 

  25. Tchokouansi, H.T., Tchidjo, R.T., Felenou, E.T., Kuetche, V.K.: Propagation of magnetic solitary waves in inhomogeneous ferrites, subjected to damping effects. J. Magn. Magn. Mater. 554, 169281 (2022)

    MATH  Google Scholar 

  26. Si, H.L., Li, B.Q.: Two types of soliton twining behaviors for the Kraenkel-Manna-Merle system in saturated ferromagnetic materials. Optik 166, 49 (2018)

    Google Scholar 

  27. Li, B.Q., Ma, Y.L., Sathishkumar, P.: The oscillating solitons for a coupled nonlinear system in nanoscale saturated ferromagnetic materials. J. Magn. Magn. Mater. 474, 661 (2019)

    Google Scholar 

  28. Younas, U., Bilal, M., Ren, J.: Diversity of exact solutions and solitary waves with the influence of damping effect in ferrites materials. J. Magn. Magn. Mater. 549, 168995 (2022)

    Google Scholar 

  29. Tchokouansi, H.T., Felenou, E.T., Tchidjo, R.T., Kuetche, V.K., Bouetou, T.B.: Traveling magnetic wave motion in ferrites: impact of inhomogeneous exchange effects. Chaos Solitons Fract. 121, 1 (2019)

    MathSciNet  MATH  Google Scholar 

  30. Li, B.Q., Ma, Y.L.: Loop-like periodic waves and solitons to the Kraenkel-Manna-Merle system in ferrites. J. Electromagn. Wave. Appl. 32, 1275 (2018)

    Google Scholar 

  31. Tchidjo, R.T., Tchokouansi, H.T., Felenou, E.T., Kuetche, V.K., Bouetou, T.B.: Influence of damping effects on the propagation of magnetic waves in ferrites. Chaos Solitons Fract. 119, 203 (2019)

    MathSciNet  MATH  Google Scholar 

  32. Randoux, S., Suret, P., Chabchoub, A., Kibler, B., El, G.: Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments. Phys. Rev. E 98, 022219 (2018)

    Google Scholar 

  33. Yang, D.Y., Tian, B., Qu, Q.X., Zhang, C.R., Chen, S.S., Wei, C.C.: Lax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiber. Chaos Solitons Fract. 150, 110487 (2021)

    MathSciNet  MATH  Google Scholar 

  34. Wu, X.H., Gao, Y.T., Yu, X., Ding, C.C., Liu, F.Y., Jia, T.T.: Darboux transformation, bright and dark-bright solitons of an \(N\)-coupled high-order nonlinear Schrödinger system in an optical fiber. Mod. Phys. Lett. B 36, 2150568 (2022)

    Google Scholar 

  35. Kengne, E., Liu, W.M., Malomed, B.A.: Spatiotemporal engineering of matter-wave solitons in Bose-Einstein condensates. Phys. Rep. 899, 1 (2021)

    MathSciNet  MATH  Google Scholar 

  36. Kumar, S., Mohan, B.: A study of multi-soliton solutions, breather, lumps, and their interactions for Kadomtsev-Petviashvili equation with variable time coefficient using Hirota method. Phys. Scr. 96, 125255 (2021)

    Google Scholar 

  37. Redor, I., Barthélemy, E., Michallet, H., Onorato, M., Mordant, N.: Experimental evidence of a hydrodynamic soliton gas. Phys. Rev. Lett. 122, 214502 (2019)

    Google Scholar 

  38. Gao, X.Y., Guo, Y.J., Shan, W.R.: Taking into consideration an extended coupled (2+1)-dimensional Burgers system in oceanography, acoustics and hydrodynamics. Chaos Solitons Fract. 161, 112293 (2022)

    MathSciNet  Google Scholar 

  39. Yang, D.Y., Tian, B., Qu, Q.X., Du, X.X., Hu, C.C., Jiang, Y., Shan, W.R.: Lax pair, solitons, breathers and modulation instability of a three-component coupled derivative nonlinear Schrödinger system for a plasma. Eur. Phys. J. Plus 137, 189 (2022)

    Google Scholar 

  40. Kumar, S., Kumar, A., Mohan, B.: Evolutionary dynamics of solitary wave profiles and abundant analytical solutions to a (3+1)-dimensional burgers system in ocean physics and hydrodynamics. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2021.11.002

    Article  Google Scholar 

  41. Zhou, T.Y., Tian, B., Zhang, C.R., Liu, S.H.: Auto-Bäcklund transformations, bilinear forms, multiple-soliton, quasi-soliton and hybrid solutions of a (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in an electron-positron plasma. Eur. Phys. J. Plus 137, 912 (2022)

  42. Wu, X.H., Gao, Y.T., Yu, X., Ding, C.C., Li, L.Q.: Modified generalized Darboux transformation and solitons for a Lakshmanan-Porsezian-Daniel equation. Chaos Solitons Fract. 162, 112399 (2022)

    MathSciNet  Google Scholar 

  43. Wang, M., Tian, B., Zhou, T.Y.: Darboux transformation, generalized Darboux transformation and vector breathers for a matrix Lakshmanan-Porsezian-Daniel equation in a Heisenberg ferromagnetic spin chain. Chaos Solitons Fract. 152, 111411 (2021)

    MathSciNet  MATH  Google Scholar 

  44. Zhou, T.Y., Tian, B., Chen, Y.Q., Shen, Y.: Painlevé analysis, auto-Bäcklund transformation and analytic solutions of a (2+1)-dimensional generalized Burgers system with the variable coefficients in a fluid. Nonlinear Dyn. 108, 2417 (2022)

    Google Scholar 

  45. Liu, F.Y., Gao, Y.T., Yu, X., Ding, C.C.: Wronskian, Gramian, Pfaffian and periodic-wave solutions for a (3+1)-dimensional generalized nonlinear evolution equation arising in the shallow water waves. Nonlinear Dyn. 108, 1599 (2022)

    Google Scholar 

  46. Shen, Y., Tian, B., Liu, S.H., Zhou, T.Y.: Studies on certain bilinear form, \(N\)-soliton, higher-order breather, periodic-wave and hybrid solutions to a (3+1)-dimensional shallow water wave equation with time-dependent coefficients. Nonlinear Dyn. 108, 2447 (2022)

    Google Scholar 

  47. Yang, D.Y., Tian, B., Wang, M., Zhao, X., Shan, W.R., Jiang, Y.: Lax pair, Darboux transformation, breathers and rogue waves of an \(N\)-coupled nonautonomous nonlinear Schrödinger system for an optical fiber or a plasma. Nonlinear Dyn. 107, 2657 (2022)

    Google Scholar 

  48. Wu, X.H., Gao, Y.T., Yu, X., Ding, C.C., Hu, L., Li, L.Q.: Binary Darboux transformation, solitons, periodic waves and modulation instability for a nonlocal Lakshmanan-Porsezian-Daniel equation. Wave Motion 114, 103036 (2022)

    MathSciNet  Google Scholar 

  49. Yang, D.Y., Tian, B., Tian, H.Y., Wei, C.C., Shan, W.R., Jiang, Y.: Darboux transformation, localized waves and conservation laws for an \(M\)-coupled variable-coefficient nonlinear Schrödinger system in an inhomogeneous optical fiber. Chaos Solitons Fract. 156, 111719 (2022)

    Google Scholar 

  50. Fan, F.C., Shi, S.Y., Xu, Z.G.: Positive and negative integrable lattice hierarchies: conservation laws and \(N\)-fold Darboux transformations. Commun. Nonlinear Sci. Numer. Simul. 91, 105453 (2020)

    MathSciNet  MATH  Google Scholar 

  51. Shen, Y., Tian, B., Zhou, T.Y., Gao, X.T.: Nonlinear differential-difference hierarchy relevant to the Ablowitz-Ladik equation: Lax pair, conservation laws, \(N\)-fold Darboux transformation and explicit exact solutions. Chaos Solitons Fract. 164, 112460 (2022)

  52. Kumar, S., Mohan, B., Kumar, A.: Generalized fifth-order nonlinear evolution equation for the Sawada–Kotera, Lax, and Caudrey–Dodd–Gibbon equations in plasma physics: Painlevé analysis and multi-soliton solutions. Phys. Scr. 97, 035201 (2022)

  53. Kumar, S., Mohan, B.: A novel and efficient method for obtaining Hirota’s bilinear form for the nonlinear evolution equation in (n+1) dimensions. Partial Differ. Equ. Appl. Math. 5, 100274 (2022)

    Google Scholar 

  54. Gao, X.T., Tian, B., Feng, C.H.: In oceanography, acoustics and hydrodynamics: investigations on an extended coupled (2+1)-dimensional Burgers system. Chin. J. Phys. 77, 2818 (2022)

    MathSciNet  Google Scholar 

  55. Gao, X.Y., Guo, Y.J., Shan, W.R.: Bilinear auto-Bäcklund transformations and similarity reductions for a (3+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama system in fluid mechanics and lattice dynamics. Qual. Theory Dyn. Syst. 21, 95 (2022)

    MATH  Google Scholar 

  56. Gao, X.T., Tian, B., Shen, Y., Feng, C.H.: Considering the shallow water of a wide channel or an open sea through a generalized (2+1)-dimensional dispersive long-wave system. Qual. Theory Dyn. Syst. 21, 104 (2022)

    MathSciNet  MATH  Google Scholar 

  57. Yang, Y.L., Fan, E.G.: Riemann-Hilbert approach to the modified nonlinear Schrödinger equation with non-vanishing asymptotic boundary conditions. Phys. D 417, 132811 (2021)

    MATH  Google Scholar 

  58. Gao, X.Y., Guo, Y.J., Shan, W.R.: Optical waves/modes in a multicomponent inhomogeneous optical fiber via a three-coupled variable-coefficient nonlinear Schrödinger system. Appl. Math. Lett. 120, 107161 (2021)

    MATH  Google Scholar 

  59. Zhou, T.Y., Tian, B., Chen, S.S., Wei, C.C., Chen, Y.Q.: Bäcklund transformations, Lax pair and solutions of a Sharma–Tasso–Olver–Burgers equation for the nonlinear dispersive waves. Mod. Phys. Lett. B 35, 2150421 (2021)

    Google Scholar 

  60. Zhou, T.Y., Tian, B.: Auto-Bäcklund transformations, Lax pair, bilinear forms and bright solitons for an extended (3+1)-dimensional nonlinear Schrödinger equation in an optical fiber. Appl. Math. Lett. 133, 108280 (2022)

    MATH  Google Scholar 

  61. Gao, X.Y., Guo, Y.J., Shan, W.R.: Auto-Bäcklund transformation, similarity reductions and solitons of an extended (2+1)-dimensional coupled Burgers system in fluid mechanics. Qual. Theory Dyn. Syst. 21, 60 (2022)

    MATH  Google Scholar 

  62. Gao, X.T., Tian, B.: Water-wave studies on a (2+1)-dimensional generalized variable-coefficient Boiti-Leon-Pempinelli system. Appl. Math. Lett. 128, 107858 (2022)

    MathSciNet  MATH  Google Scholar 

  63. Liu, F.Y., Gao, Y.T.: Lie group analysis for a higher-order Boussinesq-Burgers system. Appl. Math. Lett. 132, 108094 (2022)

    MathSciNet  MATH  Google Scholar 

  64. Liu, F.Y., Gao, Y.T., Yu, X., Hu, L., Wu, X.H.: Hybrid solutions for the (2+1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid mechanics. Chaos Solitons Fract. 152, 111355 (2021)

    MathSciNet  MATH  Google Scholar 

Download references

Funding

We express our sincere thanks to the Editors and Reviewers for their valuable comments. This work has been supported by the BUPT Excellent Ph.D. Students Foundation (No. CX2022156), by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023 and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Yuan Shen, Bo Tian, Tian-Yu Zhou & Xiao-Tian Gao

Authors
  1. Yuan Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tian-Yu Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiao-Tian Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yuan Shen or Bo Tian.

Ethics declarations

Competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this 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 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

Shen, Y., Tian, B., Zhou, TY. et al. N-fold Darboux transformation and solitonic interactions for the Kraenkel–Manna–Merle system in a saturated ferromagnetic material. Nonlinear Dyn 111, 2641–2649 (2023). https://doi.org/10.1007/s11071-022-07959-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-07959-6

Keywords

Search

Navigation