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Generalized Darboux transformation and solitons for a Kraenkel-Manna-Merle system in a ferromagnetic saturator

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Abstract

Ferromagnetic materials are considered to have the applications in data storage, data processing and telecommunication. A Kraenkel-Manna-Merle system, which describes the nonlinear electromagnetic short waves in a ferromagnetic saturator, is investigated in this paper. With respect to the magnetization related to the saturated ferromagnetic material and external magnetic field, a generalized Darboux transformation (GDT) is constructed and utilized to derive the solitons, multi-pole solitons and their interactions. Analytic expressions of the double-pole solitons are offered and analyzed via the asymptotic analysis. Then, amplitudes, characteristic lines, slopes and phase shifts of the asymptotic solitons are presented. With the multiple spectral parameters involved in the GDT, interactions among the solitons and multi-pole solitons are illustrated.

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Notes

  1. According to Ref. [7], the researchers have thought the ferromagnetic saturator as a insulator, i.e., a ferromagnetic saturator with the zero conductivity. During the derivation of System (1), effects of the current and free charge have been ignored in the Maxwell equation [7].

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Funding

We have expressed our sincere thanks to the Editors and Reviewers for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant No. 11772017.

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Authors and Affiliations

  1. Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Xi-Hu Wu, Yi-Tian Gao, Xin Yu & Fei-Yan Liu

  2. Shen Yuan Honors College, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Xi-Hu Wu

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  1. Xi-Hu Wu
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Wu, XH., Gao, YT., Yu, X. et al. Generalized Darboux transformation and solitons for a Kraenkel-Manna-Merle system in a ferromagnetic saturator. Nonlinear Dyn 111, 14421–14433 (2023). https://doi.org/10.1007/s11071-023-08510-x

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