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Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method

The nonlinear Schrödinger equation with a Dirac delta potential is considered in this paper. It is noted that the equation can be transformed into an equation with a drift-admitting jump. Then following the procedure proposed in Chen and Deng (2018 Phys. Rev. E 98 033302), a new second-order finite difference scheme is developed, which is justified by numerical examples.