A unified approach to split absorbing boundary conditions for nonlinear Schr'{o}dinger equations

摘要

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