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Formation of optical soliton wave profiles of Shynaray-IIA equation via two improved techniques: a comparative study

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Abstract

This study employs the new extended direct algebraic method and improved sardar sub-equation method to investigate solitary wave solutions in the Shynaray-IIA equation, which characterizes phenomena like tidal waves and tsunamis. These methods transform complex nonlinear coupled partial differential equations into manageable algebraic equations using a traveling wave transformation. Before this study, there is not exiting any research in which someone has obtained such kind of solutions. The main goal is to enhance understanding of the Shynaray-IIA equation behavior in various scenarios. By applying the new extended direct algebraic method and improved sardar sub-equation method, the study derives solitary wave solutions using trigonometric, hyperbolic, and Jacobi functions. By adjusting specific parameters, diverse solutions are obtained, including periodic, bell-shaped, anti-bell-shaped, M-shaped, and W-shaped solitons, each pair exhibiting mathematical symmetry. The analytical soliton solutions are further visualized in both 2D and 3D representations using Mathematica 12.3, aiding in the interpretation of these complex wave phenomena.

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Acknowledgements

This work was supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan, Grant AP14971227.

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Authors and Affiliations

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

    Waqas Ali Faridi

  2. Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

    Ghulam Hussain Tipu

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

    Zhaidary Myrzakulova & Ratbay Myrzakulov

  4. Department of Mathematics, Hampton University, Hampton, VA, USA

    Lanre Akinyemi

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  1. Waqas Ali Faridi
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  2. Ghulam Hussain Tipu
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  3. Zhaidary Myrzakulova
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  4. Ratbay Myrzakulov
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Faridi, W.A., Tipu, G.H., Myrzakulova, Z. et al. Formation of optical soliton wave profiles of Shynaray-IIA equation via two improved techniques: a comparative study. Opt Quant Electron 56, 132 (2024). https://doi.org/10.1007/s11082-023-05699-4

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