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 …

A novel class of high-order linearly implicit energy-preserving integrating factor Runge–
Kutta methods are proposed for the nonlinear Schrödinger equation. Based on the idea of …

We introduce and analyze a symmetric low-regularity scheme for the nonlinear Schrödinger
(NLS) equation beyond classical Fourier-based techniques. We show fractional …

The nonlinear Schrödinger (NLS) equation possesses an infinite hierarchy of conserved
densities, and the numerical preservation of some of these quantities is critical for accurate …

This paper considers the numerical treatment of the time-dependent Gross–Pitaevskii
equation. In order to conserve the time invariants of the equation as accurately as possible …

A large toolbox of numerical schemes for dispersive equations has been established, based
on different discretization techniques such as discretizing the variation-of-constants formula …

In this paper, we consider an energy-conserving continuous Galerkin discretization of the
Gross–Pitaevskii equation with a magnetic trapping potential and a stirring potential for …

In this paper, two novel conservative relaxation methods are developed for the space-
fractional nonlinear Schrödinger equation. The first type of relaxation scheme adopts the …

Solitons of the purely cubic nonlinear Schrödinger equation in a space dimension of n≥ 2
suffer critical and supercritical collapses. These solitons can be stabilized in a cubic-quintic …

We analyze the qualitative properties and the order of convergence of a splitting scheme for
a class of nonlinear stochastic Schrödinger equations driven by additive noise. The class of …