Investigation of Ion-Acoustic Waves in the Framework of the Schamel Burgers’ Equation Using Bifurcation Analysis

The Schamel-Burgers equation is commonly utilized in the investigation of electro trapping phenomena in plasma physics. This sort of electro trapping is more relevant in research and engineering. The equation may yield insights into the complex dynamics of nonlinear wave propagation and dissipative events in plasma physics and related domains. The Kudryashov approach reveals the solutions, which constitute prime objective of this research. Three-dimensional plots, contour plots, and two-dimensional plots are generated for the solutions. The effects of the nonlinear parameter, dissipation parameter, and time variation are also demonstrated. Furthermore, the models are transformed into a planar dynamical system using wave transformation, and the bifurcation analysis is conducted. This research highlights the adaptability of the aforementioned approach for investigating wave phenomena in engineering mathematics. Finally, the conclusion of this work carry major consequence for increasing our knowledge and analysis of nonlinear wave dynamics in different physical systems.