In this review article we discuss different techniques to solve numerically the time-dependent
Schrödinger equation on unbounded domains. We present in detail the most recent …

In this paper, we begin with the nonlinear Schrödinger/Gross–Pitaevskii equation
(NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well …

One-dimensional fractional anomalous sub-diffusion equations on an unbounded domain
are considered in our work. Beginning with the derivation of the exact artificial boundary …

Absorbing boundary conditions (ABCs) are generally required for simulating waves in
unbounded domains. As one of those approaches for designing ABCs, perfectly matched …

The aim of this paper is to describe concisely the recent theoretical and numerical
developments concerningabsorbing boundary conditions and perfectly matched layers for …

The diffusion in comb structure is an important kind of anomalous diffusion with widespread
applications. The special structure corresponds to a novel characteristic of anomalous …

Modulation instability (MI) is a pervasive phenomenon in nonlinear science. It is inevitable
for simulating rogue wave or breather solutions of the focusing nonlinear Schrödinger …

Mathematical constructions and comparisons of accurate absorbing boundary conditions for
the one-dimensional Schrödinger equation with a general variable repulsive potential are …

The numerical approximation of one-dimensional cubic nonlinear Schrödinger equations on
the whole real axis is studied in this paper. Based on the work of A. Boutet de Monvel, AS …

This paper addresses the construction of different families of absorbing boundary conditions
for the one-and two-dimensional Schrödinger equations with a general variable nonlinear …