Numerical Simulation of Rogue Waves by the Local Discontinuous Galerkin Method

We study rogue waves described by nonlinear Schr?dinger equations. Such wave solutions are so different from conventional soliton solutions that classic methods such as the Crank–Nicolson scheme cannot work for these cases. Fortunately, we find that the local discontinuous Galerkin method equipped with Dirichlet boundary conditions can simulate rogue waves very well. Several numerical examples are presented to show such interesting wave solutions.