On weakly nonlinear electron-acoustic waves in the fluid ions, bifurcation analysis, generalized symmetries and series solution propagated via Biswas–Milovic equation

In this study, various kinds of wave solutions corresponding to the conformable time-fractional Biswas–Milovic model have been obtained via the new extended direct algebraic method. The proposed approach has been used to obtain rogue wave, breather, damped wave solutions. The new extended direct algebraic method provides 37 types of soliton solution which covers almost all types of soliton families. The exact solution of the Biswas–Milovic equation can provide insights into the physical and chemical properties of the gas-solid interface. By analyzing the parameters of the equation, such as the Langmuir-Freundlich coefficient and the heterogeneity factor, researchers can gain a better understanding of the nature of the adsorption process and the properties of the porous solid. The propagation of the wave soliton possessing distinctive physical characteristics is graphically presented in 3-D plots and the dependence of the behavior of the solutions on the fractional derivative has also been analyzed which provides us with an insight into the study of wave propagation in a conformable time-fractional Biswas–Milovic model. Bifurcation analysis has been done for the governing model via Galilean transformation and phase plane portraits have been used to depict the changes in the behavior of the model by changing the values of the potential parameter. Further, novel and much more generalized Lie symmetries corresponding to the conformable time-fractional Biswas–Milovic model have been obtained and these novel symmetries have been used to obtain new reductions and power series solutions.