  In this paper we propose a method to solve the Kadomtsev--Petviashvili
equation based on splitting the linear part of the equation from the nonlinear
part. The linear part is treated using FFTs, while the nonlinear part is
approximated using a semi-Lagrangian discontinuous Galerkin approach of
arbitrary order.
  We demonstrate the efficiency and accuracy of the numerical method by
providing a range of numerical simulations. In particular, we find that our
approach can outperform the numerical methods considered in the literature by
up to a factor of five. Although we focus on the Kadomtsev--Petviashvili
equation in this paper, the proposed numerical scheme can be extended to a
range of related models as well.
