VARIATIONAL PRINCIPLE AND APPROXIMATE SOLUTION FOR THE FRACTAL GENERALIZED BENJAMIN–BONA–MAHONY–BURGERS EQUATION IN FLUID MECHANICS
Kang‐Jia Wang, Guo‐Dong Wang
Abstract
The well-known generalized Benjamin–Bona–Mahony–Burgers (gBBMB) equation is widely used in the fluid mechanics, but it becomes invalid under the non-smooth boundary. So this paper, for the first time ever, extends the gBBMB equation into the fractal form that still works under the non-smooth boundary. By using the semi-inverse method, we develop the fractal variational formulations for the problem, which can provide the conservation laws in an energy form, and reveal the possible solution structures of the equation. Furthermore, the two-scale transform method combined with the variational iteration method is used to solve the fractal gBBMB equation. The obtained results show a good agreement with the existed results.