Dynamical insights into bifurcation, chaos and solitons in the space-time fractional symmetric regularized long wave equation

Abstract The nonlinear conformable time-fractional Symmetric Regularized Long Wave (SRLW) equation is a significant model in physics, particularly for describing ion acoustic and space charge waves with weak nonlinearity. In this study, we apply the modified Sardar sub equation method and the modified extended auxiliary equation method to solve the SRLW equation. We effectively manage the fractional derivatives in the equation by employing Jumarie’s modified Riemann-Liouville derivative. Various types of soliton solutions, including kink, periodic, dark, bright, and singular solitary waves, are obtained in forms such as rational, hyperbolic, trigonometric, and exponential functions. A comparative analysis of the methods and the results is conducted, along with an exploration of fractional derivative effects by varying their values. The study also includes 2D and 3D plots that show how the solutions behave over time. It demonstrates that the methods used can be applied to other nonlinear models in mathematical physics. The research looks closely at the model’s behavior, including bifurcation, chaos, and stability. Phase portrait analysis at key points shows changes in the system’s behavior, and adding an external periodic force leads to chaotic patterns. The stability analysis proves that these methods
are reliable for studying phase portraits and soliton solutions in different nonlinear systems. Expression of concern (26 January 2026). This article is currently under investigation following a notification that raises concerns over the citations and origins of the work. As a member of COPE this is being investigated in accordance with the COPE guidelines, and as such an expression of concern is applied.