Absorbing boundary conditions for nonlinear Schrödinger equations.

A local time-splitting method (LTSM) is developed to design absorbing boundary conditions for numerical solutions of time-dependent nonlinear Schrödinger equations associated with open boundaries. These boundary conditions are significant for numerical simulations of propagations of nonlinear waves in physical applications, such as nonlinear fiber optics and Bose-Einstein condensations. Numerical examples are implemented to demonstrate the attractive features of using the LTSM.