Numerical simulation of Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equations using finite difference method

In this paper, the finite difference method is employed to solve Kadomtsev–Petviashvili–Benjamin–Bona–Mahony II (KP–BBM-II) partial differential equations. The time and space variable are discretized by the Crank–Nicholson method and the central-difference scheme, respectively. The consistence and stability are also proved. Some examples are investigated to verify the efficiency of the present method.