Assorted exact explicit solutions for the generalized Atangana’s fractional BBM–Burgers equation with the dissipative term - Hong, Baojian (Frontiers in Physics, 2022)
In this study, the generalized Atangana’s-Fractional BBM-Burgers equation(GBBM-B) with dissipative term is investigated by utilizing the modified sub-equation method and the new G'/(bG'+G+a)-expansion method, with the aid of symbolic computations, many types of new exact explicit solutions including solitary wave solutions, trigonometric function periodic solutions and the rational functions solutions are obtained. Some 3D and 2D plots about these solutions are simulated, which show the novelty and visibility of the propagation behavior and dynamical structure of the corresponding equation. Moreover, with the different values’ selection on the parameters and orders, we can deduce many types of exact solutions in special cases, we also discussed the changes and characteristics of these solutions, which can help us to further understanding the inner structure of this equation. The obtained solutions indicate that the approach is easy and effective for nonlinear models with high order dispersion terms.