Geodesic
Complex Kraenkel-Manna-Merle system in a ferrite: N-fold Darboux transformation, generalized Darboux transformation and solitons
Yuan Shen1 ; Bo Tian1 ; Tian-Yu Zhou1 ; Chong-Dong Cheng1
1 State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
Mathematical modelling of natural phenomena, Tome 18 (2023), article no. 30 Cet article a éte moissonné depuis la source EDP Sciences

Voir la notice de l'article

Ferromagnetic materials such as the ferrites are used in the electronic and energy industries. Here, we concentrate on a complex Kraenkel-Manna-Merle system in a ferrite, under some coefficient constraints. An N-fold Darboux transformation of that system is presented via an existing Lax pair, where N is a positive integer. An N-fold generalized Darboux transformation, which admits one spectral parameter, is proposed through a limit procedure. One-, two- and three-soliton solutions of that system are determined via that N-fold Darboux transformation. The second-order and third-order degenerate soliton solutions of that system are derived via that N-fold generalized Darboux transformation. Those solitons are graphically represented for the magnetization and external magnetic field related to a ferrite.
DOI : 10.1051/mmnp/2023029

Yuan Shen 1 ; Bo Tian 1 ; Tian-Yu Zhou 1 ; Chong-Dong Cheng 1

1 State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China 
@article{10_1051_mmnp_2023029,
     author = {Yuan Shen and Bo Tian and Tian-Yu Zhou and Chong-Dong Cheng},
     title = {Complex {Kraenkel-Manna-Merle} system in a ferrite: {N-fold} {Darboux} transformation, generalized {Darboux} transformation and solitons},
     journal = {Mathematical modelling of natural phenomena},
     eid = {30},
     year = {2023},
     volume = {18},
     doi = {10.1051/mmnp/2023029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2023029/}
}
TY  - JOUR
AU  - Yuan Shen
AU  - Bo Tian
AU  - Tian-Yu Zhou
AU  - Chong-Dong Cheng
TI  - Complex Kraenkel-Manna-Merle system in a ferrite: N-fold Darboux transformation, generalized Darboux transformation and solitons
JO  - Mathematical modelling of natural phenomena
PY  - 2023
VL  - 18
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2023029/
DO  - 10.1051/mmnp/2023029
LA  - en
ID  - 10_1051_mmnp_2023029
ER  - 
%0 Journal Article
%A Yuan Shen
%A Bo Tian
%A Tian-Yu Zhou
%A Chong-Dong Cheng
%T Complex Kraenkel-Manna-Merle system in a ferrite: N-fold Darboux transformation, generalized Darboux transformation and solitons
%J Mathematical modelling of natural phenomena
%D 2023
%V 18
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2023029/
%R 10.1051/mmnp/2023029
%G en
%F 10_1051_mmnp_2023029
Yuan Shen; Bo Tian; Tian-Yu Zhou; Chong-Dong Cheng. Complex Kraenkel-Manna-Merle system in a ferrite: N-fold Darboux transformation, generalized Darboux transformation and solitons. Mathematical modelling of natural phenomena, Tome 18 (2023), article  no. 30. doi: 10.1051/mmnp/2023029

[1] M.J. Ablowitz, J.T. Cole Transverse instability of rogue waves Phys. Rev. Lett 2022 104101

[2] A.N. Black, S. Choudhary, E.S. Arroyo-Rivera, H. Woodworth, R.W. Boyd Suppression of nonlinear optical rogue wave formation using polarization-structured beams Phys. Rev. Lett 2022 133902

[3] A. Bernand-Mantel, C.B. Muratov, V.V. Slastikov A micromagnetic theory of skyrmion lifetime in ultrathin ferromagnetic films Proc. Natl Acad. Sci. U.S.A. 2022 e2122237119

[4] R. Brito-Pereira, C. Ribeiro, N. Peřinka, S. Lanceros-Mendez, P. Martins Reconfigurable 3D-printable magnets with improved maximum energy product J. Mater. Chem. C 2020 952 958

[5] J.M. De Carvalho Ferreira, J.F. Gomes, G.V. Lobo, A.H. Zimerman Generalized Backlund transformations for affine Toda hierarchies J. Phys. A: Math. Theor 2021 065202

[6] I.M. Diahovchenko, R.G. Olsen Electromagnetic compatibility and protection of electric energy meters from strong magnetic fields Elec. Power Syst. Res 2020 106400

[7] H. Duran, J. Cuevas-Maraver, P.G. Kevrekidis, A. Vainchtein Discrete breathers in a mechanical metamaterial Phys. Rev. E 2023 014220

[8] A. Farolfi, D. Trypogeorgos, C. Mordini, G. Lamporesi, G. Ferrari Observation of magnetic solitons in two-component Bose-Einstein condensates Phys. Rev. Lett 2020 030401

[9] B.F. Feng, C. Shi, G. Zhang, C. Wu Higher-order rogue wave solutions of the Sasa-Satsuma equation J. Phys. A: Math. Theor 2022 235701

[10] X.Y. Gao, Oceanic shallow-water investigations on a generalized Whitham-Broer-Kaup-Boussinesq-Kupershmidt system. Phys. Fluids (2023) in press, https://doi.org/10.1063/5.0170506

[11] A.V. Gramolin, D. Aybas, D. Johnson, J. Adam, A.O. Sushkov Search for axion-like dark matter with ferromagnets Nat. Phys 2021 79 84

[12] X.W. Jin, S.J. Shen, Z.Y. Yang, J. Lin Magnetic lump motion in saturated ferromagnetic films Phys. Rev. E 2022 014205

[13] P. Joly, O. Vacus Mathematical and numerical studies of non linear ferromagnetic materials Math. Model. Numer. Anal 1999 593 626

[14] M. Kachniarz, R. Szewczyk Study on the Rayleigh hysteresis model and its applicability in modeling magnetic hysteresis phenomenon in ferromagnetic materials Acta Phys. Pol. A 2017 1244 1249

[15] B.A. Kamdem, R.K.K. Lemoula, V.K. Kuetche, J.J. Defo, R.S. Noule, S. Youssoufa Polarized waveguide excitations in microwave ferrites: the singularity structure analysis Phys. Scr 2021 115206

[16] Y.V. Kartashov, A.A. Arkhipova, S.A. Zhuravitskii, N.N. Skryabin, I.V. Dyakonov, A.A. Kalinkin, S.P. Kulik, V.O. Kompanets, S.V. Chekalin, L. Torner, V.N. Zadkov Observation of edge solitons in topological trimer arrays Phys. Rev. Lett 2022 093901

[17] R.K.K. Lemoula, B.A. Kamdem, V.K. Kuetche, R.S. Noule, J.J. Defo, S. Youssoufa Kruskal’s simplification scheme in ferrite dynamics J. Math. Phys 2021 093513

[18] B.Q. Li, Y.L. Ma Rich soliton structures for the Kraenkel-Manna-Merle (KMM) system in ferromagnetic materials J. Supercond. Nov. Magn 2018 1773 1778

[19] B.Q. Li, Y.L. Ma Loop-like periodic waves and solitons to the Kraenkel-Manna-Merle system in ferrites J. Electromagnet Waves Appl 2018 1275 1286

[20] B.Q. Li, Y.L. Ma Interaction properties between rogue wave and breathers to the manakov system arising from stationary self-focusing electromagnetic systems Chaos Solitons Fract 2022 111832

[21] B.Q. Li, Y.L. Ma Optical soliton resonances and soliton molecules for the Lakshmanan-Porsezian-Daniel system in nonlinear optics Nonlinear Dyn 2023 6689 6699

[22] B.Q. Li, Y.L. Ma A complex short pulse system in optical-fiber communications: Rogue waves and phase transitions Appl. Math. Lett. 2023 108399

[23] B.Q. Li, Y.L. Ma Oscillation rogue waves for the Kraenkel-Manna-Merle system in ferrites J. Mag. Mag. Mater 2021 168182

[24] W.X. Ma Sasa-Satsuma type matrix integrable hierarchies and their Riemann-Hilbert problems and soliton solutions Physica D 2023 133672

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

[26] Y.L. Ma, B.Q. Li Soliton resonances for a transient stimulated Raman scattering system Nonlinear Dyn 2023 2631 2640

[27] B.A. Malomed New findings for the old problem: exact solutions for domain walls in coupled real Ginzburg-Landau equations Phys. Lett. A 2022 127802

[28] S.S. Mishra, R.M. Klaes, J. Willard, R. Loloee, N.O. Birge Enhancement of supercurrent through ferromagnetic materials by interface engineering Phys. Rev. B 2022 014519

[29] F. Müller-Hoissen A vectorial binary Darboux transformation for the first member of the negative part of the AKNS hierarchy J. Phys. A: Math. Theor. 2023 125701

[30] F.T. Nguepjouo, V.K. Kuetche, T.C. Kofane Soliton interactions between multivalued localized waveguide channels within ferrites Phys. Rev. E 2014 063201

[31] Y. Shen, B. Tian, T.Y. Zhou, X.T. Gao N -fold Darboux transformation and solitonic interactions for the Kraenkel-Manna- Merle system in a saturated ferromagnetic material Nonlinear Dyn. 2023 2641 2649

[32] H.L. Si, B.Q. Li Two types of soliton twining behaviors for the Kraenkel-Manna-Merle system in saturated ferromagnetic materials Optik 2018 49 55

[33] J.M. Silveyra, E. Ferrara, D.L. Huber, T.C. Monson Soft magnetic materials for a sustainable and electrified world Science 2018 eaao0195

[34] H.T. Tchokouansi, E.T. Felenou, V.K. Kuetche, R.T. Tchidjo Dynamics of damped single valued magnetic wave in inhomogeneous circularly polarized ferrites Chin. J. Phys 2022 511 520

[35] H.T. Tchokouansi, R.T. Tchidjo, V.K. Kuetche, E.T. Felenou Propagation of single valued magnetic solitary waves in circularly polarized ferrites Chaos Solitons Fract 2022 111690

Cité par Sources :