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 …

We consider time-dependent (linear and nonlinear) Schrödinger equations in a
semiclassical scaling. These equations form a canonical class of (nonlinear) dispersive …

The goal of geometric numerical integration is the simulation of evolution equations
possessing geometric properties over long periods of time. Of particular importance are …

For classes of symplectic and symmetric time-stepping methods—trigonometric integrators
and the Störmer–Verlet or leapfrog method—applied to spectral semi-discretizations of …

We establish improved uniform error bounds for the time-splitting methods for the long-time
dynamics of the Schrödinger equation with small potential and the nonlinear Schrödinger …

Conservation properties of a full discretization via a spectral semi-discretization in space
and a Lie–Trotter splitting in time for cubic Schrödinger equations with small initial data (or …

We establish improved uniform error bounds on time-splitting methods for the long-time
dynamics of the Dirac equation with small electromagnetic potentials characterized by a …

In this paper, we consider a class of highly oscillatory Hamiltonian systems which involve a
scaling parameter. The problem arises from many physical models in some limit parameter …

Near-conservation over long times of the actions, of the energy, of the mass and of the
momentum along the numerical solution of the cubic Schrödinger equation with small initial …

Two exponential wave integrator Fourier pseudospectral (EWI-FP) methods are presented
and analyzed for the long-time dynamics of the Dirac equation with small potentials …