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Exploring the optical soliton solutions of Heisenberg ferromagnet-type of Akbota equation arising in surface geometry by explicit approach

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Abstract

This work tackles the Heisenberg ferromagnet-type integrable Akbota equation. The Akbota equation is significant model to visualize and study the surface geometry and curve analysis. The Akbota equation is an integrable coupled system of differential equations with soliton solutions. It is a crucial tool for researching nonlinear phenomena in differential geometry of curves and surfaces, magnetism, and optics. The generalized projective Riccati equation method, the Sardar sub-equation method, and the \(\frac{G^{\prime }}{G^{2}}\)-expansion method are the three separate analytical techniques used in this work. By using these approaches, exact analytical solutions for soliton waves are obtained, including dark, bright, singular, singular periodic, trigonometric, and hyperbolic waves. The creation of theoretical frameworks and the generalization of findings are made possible by analytical solutions. Researchers can frequently find patterns and relationships that apply more broadly by developing analytical solutions to particular cases, which results in the development of new theories and principles. The manuscript includes graphical representations, such as contour plots and two- or three-dimensional visualizations, in addition to theoretical derivations. These examples examine the propagation properties of the obtained soliton solutions and provide a promising basis for further research. Before this study, there is not existing any study in which, someone used these approaches and found solitons solutions.

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Acknowledgements

This work was supported by Research Supporting Project Number (RSPD2024R1007), King Saud University, Riyadh, Saudi Arabia. This work was supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan, Grant AP14971227. The author Muhammad Bilal Riaz thankful to Ministry of Education, Youth and Sports of the Czech Republic for their support through the e-INFRA CZ (ID:90254).

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Authors and Affiliations

  1. Department of Mathematics, University of Management and Technology, Lahore, Pakistan

    Waqas Ali Faridi & Muhammad Abu Bakar

  2. IT4Innovations, VSB - Technical University of Ostrava, Ostrava, Czech Republic

    Muhammad Bilal Riaz

  3. Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Astana, Kazakhstan

    Zhaidary Myrzakulova & Ratbay Myrzakulov

  4. Department of Information Systems, College Computers and Information Science, King Saud University, Riyadh, Saudi Arabia

    Almetwally M. Mostafa

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  1. Waqas Ali Faridi
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  2. Muhammad Abu Bakar
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  4. Zhaidary Myrzakulova
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Faridi, W.A., Bakar, M.A., Riaz, M.B. et al. Exploring the optical soliton solutions of Heisenberg ferromagnet-type of Akbota equation arising in surface geometry by explicit approach. Opt Quant Electron 56, 1046 (2024). https://doi.org/10.1007/s11082-024-06904-8

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