  An efficient method is proposed for numerical solutions of nonlinear
Schr\"{o}dinger equations in an unbounded domain. Through approximating the
kinetic energy term by a one-way equation and uniting it with the potential
energy equation, absorbing boundary conditions are designed to truncate the
unbounded domain, which are in nonlinear form and can perfectly absorb the
waves outgoing from the truncated domain. We examine the stability of the
induced initial boundary value problems defined on the computational domain
with the boundary conditions by a normal mode analysis. Numerical examples are
given to illustrate the stable and tractable advantages of the method.
