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Dynamics of diverse wave propagation to integrable Kraenkel–Manna–Merle system under zero damping effect in ferrites materials

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Abstract

In this study, we investigate the nonlinear dynamics of solitary waves in saturated ferromagnetic materials with an external field of zero conductivity. Here, we talk about how damping mechanisms affect the Kraenkel–Manna–Merle system, which controls wave propagation and expresses nonlinear ultra-short wave pulse movements in ferromagnetic materials. By using a good computational integration method called the extended Fan-sub equation technique, a number of solitary wave solutions in diverse shapes, such as hyperbolic, Jacobi’s elliptic, and trigonometric functions solutions are found. Not only do we protect periodic solutions with unknown parameters, but we also extract bell, kink, singular mixed complicated solitons. These findings demonstrate the theoretically incredibly rich soliton structures present in the system. For clarity in comprehending the solutions generated with the values of unknown parameters, two-dimensional, three-dimensional, and their contour wave profiles are plotted. The findings reveal that the integration method utilized is clear and may be extended to more complicated phenomena by using symbolic computations.

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Data Availibility Statement

This study did not use any data.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 52071298), the Strategic Research and Consulting Project of Chinese Academy of Engineering (No. 2022HENYB05), the ZhongYuan Science and Technology Innovation Leadership Program (No. 214200510010). This research is supported by Researchers Supporting Project Number (RSP2023R158), King Saud University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Henan Academy of Big Data/School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

    Muhammad Bilal & Jingli Ren

  2. Department of Mathematics, Science Faculty, Firat University, 23119, Elazig, Turkey

    Mustafa Inc

  3. Department of Medical Research, China Medical University, Taichung, 40402, Taiwan

    Mustafa Inc

  4. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia

    Bandar Almohsen

  5. Department of Mathematics, Lafayette College, Easton, PA, USA

    Lanre Akinyemi

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  1. Muhammad Bilal
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  4. Bandar Almohsen
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All authors contributed to the study conception and design. All authors read and approved the final manuscript.

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Bilal, M., Ren, J., Inc, M. et al. Dynamics of diverse wave propagation to integrable Kraenkel–Manna–Merle system under zero damping effect in ferrites materials. Opt Quant Electron 55, 646 (2023). https://doi.org/10.1007/s11082-023-04879-6

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