Exact nonreflecting boundary conditions for one-dimensional cubic nonlinear Schrödinger equations

The numerical approximation of one-dimensional cubic nonlinear Schrödinger equations on the whole real axis is studied in this paper. Based on the work of A. Boutet de Monvel, A.S. Fokas and D. Shepelsky [Lett. Math. Phys., 65(3): 199–212, 2003], a kind of exact nonreflecting boundary conditions are derived on the artificially introduced boundary points. The related numerical issues are discussed in detail. Several numerical tests are performed to demonstrate the behaviour of the proposed scheme.