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Absorbing Boundary Conditions for One-dimensional Nonlinear Schrödinger Equations

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Abstract

We construct two families of absorbing boundary conditions for the nonlinear Schrödinger equation. The first one relies on the pseudodifferential calculus and the second one relies on the paradifferential calculus. We show that some of the corresponding initial boundary value problems are well-posed. We finally present numerical experiments illustrating the efficiency of these methods.

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  1. Jérémie Szeftel

    Present address: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ, 08544-1000, USA

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  1. LAGA UMR 7539, Institut Galilée, Université Paris 13, 99, avenue J.B.Clément, 93430, Villetaneuse, France

    Jérémie Szeftel

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  1. Jérémie Szeftel
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Szeftel, J. Absorbing Boundary Conditions for One-dimensional Nonlinear Schrödinger Equations. Numer. Math. 104, 103–127 (2006). https://doi.org/10.1007/s00211-006-0012-7

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  • DOI: https://doi.org/10.1007/s00211-006-0012-7

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