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 …

In this paper, we study linearized Crank–Nicolson Galerkin FEMs for a generalized
nonlinear Schrödinger equation. We present the optimal L^ 2 L 2 error estimate without any …

In this paper, we propose new efficient and accurate numerical methods for computing dark
solitons and review some existing numerical methods for bright and/or dark solitons in the …

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

We study the defocusing nonlinear Schrödinger (NLS) equation written in hydrodynamic
form through the Madelung transform. From the mathematical point of view, the …

The paper is concerned with the time step condition of the commonly-used semi-implicit
Crank–Nicolson finite difference schemes for a coupled nonlinear Schrödinger system in …

The aim of this paper is to design some accurate artificial boundary conditions for the semi-
discretized linear Schrödinger and heat equations in rectangular domains. The Laplace …

Recently, we have developed a generalized finite-difference time-domain (G-FDTD) method
for solving the time dependent linear Schrödinger equation. The G-FDTD is explicit and …

The paper is concerned with the unconditional stability and optimal L^ 2 L 2 error estimates
of linearized Crank–Nicolson Galerkin FEMs for a nonlinear Schrödinger–Helmholtz system …

To simulate waves on unbounded domain, absorbing boundary conditions are usually
needed to bound the computational domain and avoid boundary reflections as much as …