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Numerical solution to coupled nonlinear Schrödinger equations on unbounded domains

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  • Zhou, Shenggao
  • Cheng, Xiaoliang

Abstract

The numerical simulation of coupled nonlinear Schrödinger 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 Schrödinger 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.

Suggested Citation

  • Zhou, Shenggao & Cheng, Xiaoliang, 2010. "Numerical solution to coupled nonlinear Schrödinger equations on unbounded domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2362-2373.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:12:p:2362-2373
    DOI: 10.1016/j.matcom.2010.05.019
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    1. Ismail, M.S. & Taha, Thiab R., 2001. "Numerical simulation of coupled nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(6), pages 547-562.
    2. Ismail, M.S., 2008. "Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 532-547.
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    Cited by:

    1. Ilati, Mohammad & Dehghan, Mehdi, 2019. "DMLPG method for numerical simulation of soliton collisions in multi-dimensional coupled damped nonlinear Schrödinger system which arises from Bose–Einstein condensates," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 244-253.

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