Numerical solution of the general coupled nonlinear Schr?dinger equations on unbounded domains

摘要

The numerical solution of the general coupled nonlinear Schr?dinger equations on unbounded domains isconsidered by applying the artificial boundary method in this paper. In order to design the local absorbing boundaryconditions for the coupled nonlinear Schr?dinger equations, we generalize the unified approach previouslyproposed [J. Zhang et al., Phys. Rev. E 78, 026709 (2008)]. Based on the methodology underlying the unifiedapproach, the original problem is split into two parts, linear and nonlinear terms, and we then achieve a one-wayoperator to approximate the linear term to make the wave out-going, and finally we combine the one-way operatorwith the nonlinear term to derive the local absorbing boundary conditions. Then we reduce the original probleminto an initial boundary value problem on the bounded domain, which can be solved by the finite differencemethod. The stability of the reduced problem is also analyzed by introducing some auxiliary variables. Amplenumerical examples are presented to verify the accuracy and effectiveness of our proposed method.