Unified approach to split absorbing boundary conditions for nonlinear Schrödinger equations: Two-dimensional case

This paper aims to design local absorbing boundary conditions (LABCs) for the two-dimensional nonlinear Schrödinger equations on a rectangle by extending the unified approach. Based on the time-splitting idea, the main process of the unified approach is to approximate the kinetic energy part by a one-way equation, unite it with the potential energy equation, and then obtain the well-posed and accurate LABCs on the artificial boundaries. In the corners, we use the (1,1)-Padé approximation to the kinetic term and also unite it with the nonlinear term to give some local corner boundary conditions. Numerical tests are given to verify the stable and tractable advantages of the method.

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