A perfectly matched layer approach to the nonlinear Schrödinger wave equations

Absorbing boundary conditions (ABCs) are generally required for simulating waves in unbounded domains. As one of those approaches for designing ABCs, perfectly matched layer (PML) has achieved great success for both linear and nonlinear wave equations. In this paper we apply PML to the nonlinear Schrödinger wave equations. The idea involved is stimulated by the good performance of PML for the linear Schrödinger equation with constant potentials, together with the time-transverse invariant property held by the nonlinear Schrödinger wave equations. Numerical tests demonstrate the effectiveness of our PML approach for both nonlinear Schrödinger equations and some Schrödinger-coupled systems in each spatial dimension.