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, an energy conservative Crank–Nicolson difference scheme for nonlinear Riesz
space-fractional Schrödinger equations is studied. We give a rigorous analysis of the …

A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-
dimensional nonlinear Schrödinger equation. By establishing the equivalence between the …

In this paper, a class of nonlinear Riesz space-fractional Schrödinger equations are
considered. Based on the standard Galerkin finite element method in space and Crank …

Nonlinear evolution equations are widely used to describe nonlinear phenomena in natural
and social sciences. However, they are usually quite difficult to solve in most instances. This …

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 …

In this work, the error splitting technique combined with cut-off function method is designed
to derive unconditionally optimal error estimates for a fully implicit conservative numerical …

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 present, in a unified framework, conforming and nonconforming virtual element methods
for nonlinear Schrödinger equation. The constructed schemes conserve not only the mass …

In this paper, we first construct an appropriate new generating function, and then based on
this function, we establish a fourth-order numerical differential formula approximating the …