Numerical solution to coupled nonlinear Schrodinger equations on unbounded domains
The numerical simulation of coupled nonlinear Schrodinger equations on unbounded domains is considered in this paper. By using the operator splitting technique, the original problem is decomposed into linear and nonlinear subproblems in a small time step. The linear subproblem turns out to be two decoupled linear Schrodinger equations on unbounded domains, where artificial boundaries are introduced to truncate the unbounded physical domains into finite ones. Local absorbing boundary conditions are imposed on the artificial boundaries. On the other hand, the coupled nonlinear subproblem is an ODE system, which can be solved exactly. To demonstrate the effectiveness of our method, some comparisons in terms of accuracy and computational cost are made between the PML approach and our method in numerical examples. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
coupled nonlinear schrodinger equations unbounded domain absorbing boundary condition operator splitting method soliton