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The optical exact soliton solutions of Shynaray-IIA equation with \(\Phi ^6\)-model expansion approach

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Abstract

This paper investigates the Shynaray-IIA equation (S-IIAE), a type of partial differential parametric equation, using the \(\Phi ^6\)-model expansion method. The Shynaray-IIA equation is coupled system of differential equations which is integrable and contain soliton solutions. It addresses the integrable motion of space curves and have a lot of applications in nonlinear optics, water waves, plasma physics and other modern sciences. Prior to this study, no previous research has achieved solutions of this kind. In order to fill this gap, the \(\Phi ^6\)-model expansion method is employing to Shynaray-IIA equation and obtains new exact solutions for the perturbed form of the Shynaray-IIA equation, including bright, singular, periodic, and combined singular soliton solutions. These findings enhance our understanding of the equation’s nonlinear dynamical properties and offer a practical and efficient approach to solving various nonlinear partial differential equations. The research also explores specific parameter values that meet constraint conditions to reveal the dynamic behavior of the solutions. To present these findings effectively, the study utilizes visually appealing graphs that highlight the solutions’ characteristics. Overall, this work contributes to advancing our knowledge of the Shynaray-IIA equation and demonstrates the applicability of the \(\Phi ^6\)-model expansion method in studying nonlinear systems.

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Acknowledgements

This work was supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan, Grant AP14870191.

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Authors and Affiliations

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

    Ghulam Hussain Tipu

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

    Waqas Ali Faridi

  3. Department of Mathematics, College of Science and Arts, Qassim University, Al-Asyah, Saudi Arabia

    Doaa Rizk

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

    Zhaidary Myrzakulova & Ratbay Myrzakulov

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

    Lanre Akinyemi

Authors
  1. Ghulam Hussain Tipu
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  2. Waqas Ali Faridi
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  3. Doaa Rizk
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  4. Zhaidary Myrzakulova
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  5. Ratbay Myrzakulov
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  6. Lanre Akinyemi
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Contributions

Formal analysis, problem formulation W.A.F, L.A; Investigation, Methodology G.H.T, and W.A.F, Supervision, resources; Z.M, and R.M, Validation, graphical discussion and software; L.A, G.H.T, Z.M, R.M, and W.A.F. Review and editing; all authors approved the final version for submission.

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Correspondence to Waqas Ali Faridi.

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Tipu, G.H., Faridi, W.A., Rizk, D. et al. The optical exact soliton solutions of Shynaray-IIA equation with \(\Phi ^6\)-model expansion approach. Opt Quant Electron 56, 226 (2024). https://doi.org/10.1007/s11082-023-05814-5

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