Nonlinear systems with periodic variations of nonlinearity and/or dispersion occur in a
variety of physical problems and engineering applications. The mathematical concept of …

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 …

Optical frequency combs are one of the most remarkable inventions in recent decades.
Originally conceived as the spectral counterpart of the train of short pulses emitted by mode …

Optical collapse is a fascinating research topic. The propagation of intense laser beams in a
transparent medium is usually modeled by the two-dimensional nonlinear Schrödinger …

We give an error analysis of Strang-type splitting integrators for nonlinear Schrödinger
equations. For Schrödinger-Poisson equations with an $ H^ 4$-regular solution, a first-order …

We approximate the solutions of an initial-and boundary-value problem for nonlinear
Schrödinger equations (with emphasis on the 'cubic'nonlinearity) by two fully discrete finite …

We use a multiple time scale boundary layer theory to derive the equation of motion for a
dark (or grey) soliton propagating through an effectively one-dimensional cloud of Bose …

First-quantized, grid-based methods for chemistry modeling are a natural and elegant fit for
quantum computers. However, it is infeasible to use today's quantum prototypes to explore …

Operator splitting (or the fractional steps method) is a very common tool to analyze nonlinear
partial differential equations both numerically and analytically. By applying operator splitting …

We propose a compact split-step finite difference method to solve the nonlinear Schrödinger
equations with constant and variable coefficients. This method improves the accuracy of split …