Absorbing Boundary Conditions for General Nonlinear Schrödinger Equations

Xavier Antoine (1, 2) , Christophe Besse (3, 4) , Pauline Klein (5)

1 IECN - Institut Élie Cartan de Nancy
2 CORIDA - Robust control of infinite dimensional systems and applications
3 LPP - Laboratoire Paul Painlevé - UMR 8524
4 SIMPAF - SImulations and Modeling for PArticles and Fluids
5 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

This paper addresses the construction of different families of absorbing boundary conditions for the one- and two-dimensional Schrödinger equation with a general variable nonlinear potential. Various semi-discrete time schemes are built for the associated initial boundary value problems. Finally, some numerical simulations give a comparison of the various absorbing boundary conditions and associated schemes to analyze their accuracy and efficiency.

Mots clés: absorbing boundary conditions; pseudodifferential operators; stable semi-discrete schemes; nonlinear Schrödinger equation with potential; fixed point algorithm; relaxation scheme

Domaines: Analyse numérique [math.NA]; Mathématiques générales [math.GM]

Xavier Antoine, Christophe Besse, Pauline Klein. Absorbing Boundary Conditions for General Nonlinear Schrödinger Equations. SIAM Journal on Scientific Computing, 2011, 33 (2), pp.1008-1033. ⟨10.1137/090780535⟩. ⟨hal-00755578⟩