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

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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.

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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.

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  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

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  1. Yuan Shen
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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

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