A splitting approach for the Kadomtsev-Petviashvili equation

We consider a splitting approach for the Kadomtsev–Petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure can be efficiently implemented. The error made by this numerical scheme is compared to exponential integrators which have been shown in Klein and Roidot (SIAM J. Sci. Comput., 2011) to perform best for stiff solutions of the Kadomtsev–Petviashvili equation. Since splitting methods are limited to order two in this case, we propose a stable extrapolation method in order to construct a numerical scheme of order four. In addition, the conservation properties of the numerical schemes under consideration are investigated.