High-order numerical method for the derivative nonlinear Schrödinger equation

In this work, a fourth-order numerical scheme in space and two second-order numerical schemes in both time and space are proposed for the derivative nonlinear Schrodinger equation. We verify the mass conservation for the two-level implicit scheme. The influence on the soliton solution by adding a small random perturbation to the initial condition is discussed. The numerical experiments are given to test the accuracy order for different schemes, respectively. We also test the conservative property of mass and Hamiltonian for these schemes from the numerical point of view.