In this paper, we mainly review recent results on mathematical theory and numerical
methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation …

We perform a survey of some recent theoretical and experimental studies on
multidimensional (two-and three-dimensional) localized structures in optical and matter …

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 …

Abstract The (3+ 1)-dimensional generalized shallow water wave equation is systematically
investigated in this paper based on the Hirota bilinear method. The N-soliton solution and …

In this paper, a linearly implicit conservative difference scheme for the coupled nonlinear
Schrödinger equations with space fractional derivative is proposed. This scheme conserves …

In this paper, based on the Scalar Auxiliary Variable (SAV) approach [44],[45] and a newly
proposed Lagrange multiplier (LagM) approach [22],[21] originally constructed for gradient …

Many of the static and dynamic properties of an atomic Bose–Einstein condensate (BEC) are
usually studied by solving the mean-field Gross–Pitaevskii (GP) equation, which is a …

A family of arbitrarily high-order fully discrete space-time finite element methods are
proposed for the nonlinear Schrödinger equation based on the scalar auxiliary variable …

We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for
the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the …

Investigated in this paper is the defocusing nonlinear Schrödinger (NLS) equation, which is
used for describing the wave-packet dynamics in certain weakly nonlinear media. With the …