A LDG method for the fourth-order NLS equation

In this paper, a local discontinuous Galerkin (LDG) method is is designed for solving the BBM-Burgers equation with four-order spatial derivatives. Our schemes extend the previous work of Xu and Shu [8] solving the nonlinear Schrödinger equations on LDG method. The L
²
stability of the LDG methods is proved for general solutions. Numerical results are shown to illustrate the accuracy and capability of the LDG method.