Fourth-Order Compact Split-Step Finite Difference Method for Solving the Two- and Three-Dimensional Nonlinear Schrödinger Equations

In this paper we show a fourth-order compact split-step finite difference method to solve the two- and three-dimensional nonlinear Schrödinger equations. The conservation properties and stability are analyzed for the proposed scheme. Numerical results show that the method can provide accurate and stable solutions for the nonlinear Schrödinger equation.