Stability analysis, bifurcation and chaotic dynamics, and analytical soliton solutions of the modified RLW-Burgers equation using an expansion scheme

In this article, we investigate the modified regularized long wave-Burgers (RLW-Burgers) equation in the context of nonlinear wave propagation, integrating nonlinearity, dissipation, and dispersion. Using the systematic (F′/F, 1/F)-expansion approach, we construct a large class of exact soliton solutions, such as bell-shaped, cuspon, compacton, periodic, V-shaped, parabolic, breather, and pulse-type solitons. The physical attributes of the obtained solutions are illustrated through two- and three-dimensional graphical representations, exhibiting their structural variability and relevance to shallow water waves, plasma physics, and fluid flows. Furthermore, we conduct stability analysis to examine the persistence of the solution and the sensitivity of the wave velocity to system parameters and explore equilibrium states, bifurcations, and transcritical bifurcation. We also analyze chaotic dynamics by applying periodic forces, revealing transitions between periodic, quasi-periodic, and chaotic regimes. Comparative analysis with existing results underscores the novelty and physical significance of the solutions, thereby contributing to an insightful theoretical understanding of nonlinear dispersive and diffusive wave systems.