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Exact Soliton Solutions and Complex Dynamical Analysis of the Nonlinear Model Arising in Mathematical Physics

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  • Badr Saad T. Alkahtani

Abstract

This study investigates the 1+1-dimensional Sharma–Tasso–Olver–Burgers (STOB) equation, a nonlinear model arising in mathematical physics. The modified F-expansion method is employed to derive a variety of exact soliton solutions, including trigonometric, hyperbolic, singular, periodic, and exponential forms. In addition to analytical solution construction, the dynamical behavior of the model is examined through bifurcation and chaos analysis. Quantitative and qualitative tools such as return maps, power spectra, and time series are utilized to characterize the system dynamics and identify transitions to chaotic regimes. The results demonstrate that the proposed approach is efficient and reliable, providing new insights into nonlinear wave structures and complex dynamical phenomena in nonlinear systems.

Suggested Citation

  • Badr Saad T. Alkahtani, 2026. "Exact Soliton Solutions and Complex Dynamical Analysis of the Nonlinear Model Arising in Mathematical Physics," Advances in Mathematical Physics, Hindawi, vol. 2026, pages 1-14, September.
    • Handle: RePEc:hin:jnlamp:2834329
    DOI: 10.1155/admp/2834329
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