High-order conservative schemes for the nonlinear Schrödinger equation in the semiclassical limit

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx) General mathematical topics and methods in quantum theory (81Qxx)

Cites Work

Unnamed Item
Unnamed Item
Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime
Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap
On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit. II. Analytic regularity
Generalized integrating factor methods for stiff PDEs
Optimal convergence analysis of the energy-preserving immersed weak Galerkin method for second-order hyperbolic interface problems in inhomogeneous media
Difference schemes for solving the generalized nonlinear Schrödinger equation
The nonlinear Schrödinger equation. Self-focusing and wave collapse
Semi-classical limit of a Schrödinger equation for a stratified material
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
Solution of multi-dimensional Klein-Gordon-Zakharov and Schrödinger/Gross-Pitaevskii equations via local radial basis functions-differential quadrature (RBF-DQ) technique on non-rectangular computational domains
A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method
A numerical study of the semi-classical limit of the focusing nonlinear Schrödinger equation
DMLPG method for numerical simulation of soliton collisions in multi-dimensional coupled damped nonlinear Schrödinger system which arises from Bose-Einstein condensates
Efficient dissipation-preserving approaches for the damped nonlinear Schrödinger equation
Scalar auxiliary variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations
Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs
Mathematical and computational methods for semiclassical Schrödinger equations
Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
The numerical integration of relative equilibrium solutions. The nonlinear Schrodinger equation
A Relaxation Scheme for the Nonlinear Schrödinger Equation
Geometric Numerical Integration
Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
Compact Exponential Conservative Approaches for the Schrödinger Equation in the Semiclassical Regimes
Computing quantum dynamics in the semiclassical regime