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<p>In order to analyze the induced space curves with integrable motion governed by this model, this study focuses on finding different types of soliton solutions for the integrable Shynaray-IIA problem. Due to their applications in various physical phenomena, such as optical fibers, nonlinear optics, and ferromagnetic materials, the solitons derived from the Shynaray-IIA equation are important. Two different analytical schemes are used to create these various soliton forms: the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\frac{G^{\prime}}{G^{\prime}+G+A})\)</EquationSource> </InlineEquation>-expansion scheme and the extended simple equation scheme. Newly derived soliton solutions in the form of periodic trigonometric, parabolic, unique W‑shaped, and M‑shaped soliton structures are presented in this study. According to our analysis of the literature, these approaches are novel for the aforementioned equation. The resulting solutions offer a&#xa0;useful framework for studying nonlinear spin dynamics in magnetic systems, plasma physics, quantum field theory, and fluid dynamics. Furthermore, the differential transform method is used to perform numerical simulations of the resulting soliton solutions. A&#xa0;comparison between the related numerical approximations and the analytical soliton solutions is also provided.</p>

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Analytical and numerical solutions of the integrable Shynaray-IIA equation: solitary wave dynamics in fiber optics

  • 期刊论文

  • 发表日期：

    2026年5月4日

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  • Sana Anwar,
  • Asim Zafar

摘要

In order to analyze the induced space curves with integrable motion governed by this model, this study focuses on finding different types of soliton solutions for the integrable Shynaray-IIA problem. Due to their applications in various physical phenomena, such as optical fibers, nonlinear optics, and ferromagnetic materials, the solitons derived from the Shynaray-IIA equation are important. Two different analytical schemes are used to create these various soliton forms: the \((\frac{G^{\prime}}{G^{\prime}+G+A})\) -expansion scheme and the extended simple equation scheme. Newly derived soliton solutions in the form of periodic trigonometric, parabolic, unique W‑shaped, and M‑shaped soliton structures are presented in this study. According to our analysis of the literature, these approaches are novel for the aforementioned equation. The resulting solutions offer a useful framework for studying nonlinear spin dynamics in magnetic systems, plasma physics, quantum field theory, and fluid dynamics. Furthermore, the differential transform method is used to perform numerical simulations of the resulting soliton solutions. A comparison between the related numerical approximations and the analytical soliton solutions is also provided.