Computational methods for the dynamics of the nonlinear Schrödinger/Gross–Pitaevskii equations
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 …
(NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well …
Mathematical and computational methods for semiclassical Schrödinger equations
We consider time-dependent (linear and nonlinear) Schrödinger equations in a
semiclassical scaling. These equations form a canonical class of (nonlinear) dispersive …
semiclassical scaling. These equations form a canonical class of (nonlinear) dispersive …
[图书][B] Geometric numerical integration and Schrödinger equations
E Faou - 2012 - books.google.com
The goal of geometric numerical integration is the simulation of evolution equations
possessing geometric properties over long periods of time. Of particular importance are …
possessing geometric properties over long periods of time. Of particular importance are …
Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations
For classes of symplectic and symmetric time-stepping methods—trigonometric integrators
and the Störmer–Verlet or leapfrog method—applied to spectral semi-discretizations of …
and the Störmer–Verlet or leapfrog method—applied to spectral semi-discretizations of …
Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation
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 …
dynamics of the Schrödinger equation with small potential and the nonlinear Schrödinger …
Splitting integrators for nonlinear Schrödinger equations over long times
L Gauckler, C Lubich - Foundations of Computational Mathematics, 2010 - Springer
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 …
and a Lie–Trotter splitting in time for cubic Schrödinger equations with small initial data (or …
Improved uniform error bounds on time-splitting methods for the long-time dynamics of the Dirac equation with small potentials
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 …
dynamics of the Dirac equation with small electromagnetic potentials characterized by a …
Geometric two-scale integrators for highly oscillatory system: uniform accuracy and near conservations
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 …
scaling parameter. The problem arises from many physical models in some limit parameter …
One-stage exponential integrators for nonlinear Schrödinger equations over long times
D Cohen, L Gauckler - BIT Numerical Mathematics, 2012 - Springer
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 …
momentum along the numerical solution of the cubic Schrödinger equation with small initial …
Uniform error bounds of exponential wave integrator methods for the long-time dynamics of the Dirac equation with small potentials
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 …
and analyzed for the long-time dynamics of the Dirac equation with small potentials …