Numerical Solution Of Coupled Nonlinear Schr(?)dinger Equations On Unbounded Domains

In this paper,we mainly study the numerical solution for the coupled nonlin-ear Schr(?)dinger equations on unbounded domains,which arise in many important fields,such as optical fiber propagation,plasma physics,superconductivity and deep water waves.In recent years,the coupled nonlinear Schr(?)dinger equations have aroused extensive attention and research by many scholars all over the world.However,it is difficult to solve directly the original problem defined on unbound-ed domains,since the physical domain is unbounded and the coupled nonlinear Schr(?)dinger equations are nonlinear.To overcome the difficulties,the appropri-ate local artificial boundary conditions are designed on the introduced artificial boundaries by applying the idea of the operator splitting method.Then the orig-inal problem defined on unbounded domains is reduced into an initial boundary value problem on the bounded computational domains,which can be solved by the finite difference method.The stability of the reduced problem and the cor-responding discretized system is analyzed by introducing some auxiliary variables and constructing mass function.Ample numerical results are presented to verify the accuracy and effectiveness of the proposed methods,and the propagations for the nonlinear coupled Schr(?)dinger equations on unbounded domains are simulated.