Numerical simulation of solitons and dromions in the Davey–Stewartson system

We extend the well-known split-step Fourier method for solving the nonlinear Schrödinger equation to the Davey–Stewartson system. We discuss both the elliptic-hyperbolic and hyperbolic-elliptic cases, as well as the implementation of boundary conditions. Numerical tests, including the simulation of rational solitons and dromions, are presented.