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The analytical study of soliton dynamics in fractional coupled Higgs system using the generalized Khater method

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Abstract

This study introduces the generalized Khater Method (gKM) as a tool for investigating the existence and dynamics of soliton solutions within the realm of the Fractional Coupled Higgs System (FCHS) with conformable fractional derivatives. The methodology involves obtaining Nonlinear Ordinary Differential Equations (NODEs) from FCHS via a fractional complex transformation. The reduced NODEs are further used to uncover various families of soliton solutions, elucidating their intricate interrelationships and dynamics. Using some 3D graphics, we visually depict the behavior of some soliton solutions, including shock, lump-type shock, periodic, multiple periodic, rogue, and kink solitons. These findings contribute to a better understanding of the dynamics inherent in the FCHS and have potential applications in domains dealing with nonlinear fractional partial differential equations. Arguably, the study also highlights the importance of incorporating the conformable fractional derivative into the FCHS to provide it with more degrees of freedom, which allows for a deeper exploration of its behaviors and could have significant implications for particle physics, particularly for phenomena such as mass origin and electroweak violation of symmetry.

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The data that support the findings of this study are available upon reasonable request.

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Acknowledgements

The authors express their gratitude to the Deanship of Scientific Research at King Khalid University for funding this work through the Large Research Groups Project under Grant No. RGP. 1/184/44.

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Authors and Affiliations

  1. School of Mathematical Science, Zhejiang Normal University, Jinhua, 321004, Zhejiang, People’s Republic of China

    Rashid Ali & Zhao Zhang

  2. Operational Research Center in Healthcare, Near East University, TRNC Mersin 10, Nicosia, 99138, Turkey

    Hijaz Ahmad

  3. Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia

    Hijaz Ahmad

  4. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Hijaz Ahmad

  5. Department of Basic Medical Sciences, College of Applied Medical Science, King Khalid University, 61421, Abha, Saudi Arabia

    Mohammad Mahtab Alam

  6. Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, Mishref, Kuwait

    Hijaz Ahmad

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  1. Rashid Ali
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Contributions

Conceptualization: RA. Data curation: ZZ. Formal analysis: RA and MMA. Validation: ZZ and HA. Writing-original draft: RA and ZZ. Writing-review editing: HA.

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Correspondence to Hijaz Ahmad.

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Ali, R., Zhang, Z., Ahmad, H. et al. The analytical study of soliton dynamics in fractional coupled Higgs system using the generalized Khater method. Opt Quant Electron 56, 1067 (2024). https://doi.org/10.1007/s11082-024-06924-4

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