Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations

This paper addresses the construction of nonlinear integro-differential artificial boundary conditions for one-dimensional nonlinear cubic Schrödinger equations. Several ways of designing such conditions are provided and a theoretical classification of their accuracy is given. Semidiscrete time schemes based on the method developed by Durán and Sanz-Serna [IMA J. Numer. Anal. 20 (2000), pp. 235-261] are derived for these unusual boundary conditions. Stability results are stated and several numerical tests are performed to analyze the capacity of the proposed approach.

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