A unified approach to split absorbing boundary conditions for nonlinear Schrödinger equations

Details A unified approach to split absorbing boundary conditions for nonlinear Schrödinger equations A unified approach to split absorbing boundary conditions for nonlinear Schrödinger equations

2008-06-11

arxiv.org/abs/0806.1854v1

Mathematics

Numerical Analysis

17 pages, 6 figures, 40 conferences

Scientific paper

10.1103/PhysRevE.78.026709

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.

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