#### 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. Mathematics Subject Classification (2000) 35Q55 · 35S50 · 35A21 · 35A07 · 65M99