An Explicit Unconditionally Stable Numerical Method for Solving Damped Nonlinear Schrödinger Equations with a Focusing Nonlinearity
From MaRDI portal
Publication:4443654
DOI10.1137/S0036142902413391zbMath1054.35088arXivmath/0303158MaRDI QIDQ4443654
Publication date: 18 January 2004
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0303158
Gross-Pitaevskii equationBose-Einstein condensatecomplex Ginzburg-Landau equationdamped nonlinear Schrödinger equationtime-splitting sine-spectral method
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) NLS equations (nonlinear Schrödinger equations) (35Q55) Computational methods for problems pertaining to quantum theory (81-08) Numerical methods for trigonometric approximation and interpolation (65T40)
Related Items
Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation ⋮ Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term ⋮ Segregated nodal domains of two-dimensional multispecies Bose-Einstein condensates ⋮ An efficient and stable numerical method for the Maxwell--Dirac system ⋮ Convergence of compact ADI method for solving linear Schrödinger equations ⋮ A time-splitting spectral method for coupled Gross-Pitaevskii equations with applications to rotating Bose-Einstein condensates ⋮ Numerical study of fourth-order linearized compact schemes for generalized NLS equations ⋮ Galerkin finite element method for damped nonlinear Schrödinger equation ⋮ Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations ⋮ Efficient and accurate numerical methods for the Klein-Gordon-Schrödinger equations ⋮ An adaptive multigrid scheme for Bose-Einstein condensates in a periodic potential ⋮ A time-splitting pseudospectral method for the solution of the Gross-Pitaevskii equations using spherical harmonics with generalised-Laguerre basis functions ⋮ Computing multiple peak solutions for Bose-Einstein condensates in optical lattices ⋮ Efficient dissipation-preserving scheme for the damped nonlinear Schrödinger equation in three dimensions ⋮ An efficient Chebyshev-tau spectral method for Ginzburg-Landau-Schrödinger equations ⋮ Efficient schemes for the damped nonlinear Schrödinger equation in high dimensions ⋮ Crank-Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative ⋮ An efficient energy-stable pseudospectral method for simulating vortex dynamics of the Ginzburg-Landau-Schrödinger equation ⋮ A positivity preserving iterative method for finding the ground states of saturable nonlinear Schrödinger equations ⋮ Numerical methods for the generalized Zakharov system. ⋮ A radial basis function-Hermite finite difference (RBF-HFD) method for the cubic-quintic complex Ginzburg-Landau equation ⋮ A high-order accurate wavelet method for solving Schrödinger equations with general nonlinearity ⋮ Convergence of an eighth-order compact difference scheme for the nonlinear Schrödinger equation ⋮ An efficient split-step compact finite difference method for cubic-quintic complex Ginzburg-Landau equations ⋮ A linearly implicit structure-preserving Fourier pseudo-spectral scheme for the damped nonlinear Schrödinger equation in three dimensions ⋮ Review Article: Mathematical Models and Numerical Methods for Spinor Bose-Einstein Condensates ⋮ A space-time fully decoupled wavelet Galerkin method for solving multidimensional nonlinear Schrödinger equations with damping ⋮ Dynamics of a Gross-Pitaevskii equation with phenomenological damping ⋮ Maximum-norm error analysis of a conservative scheme for the damped nonlinear fractional Schrödinger equation ⋮ On a conservative Fourier spectral Galerkin method for cubic nonlinear Schrödinger equation with fractional Laplacian ⋮ New numerical methods for the coupled nonlinear Schrödinger equations ⋮ The limit behavior of solutions for the nonlinear Schrödinger equation including nonlinear loss/gain with variable coefficient ⋮ Almost structure-preserving analysis for weakly linear damping nonlinear Schrödinger equation with periodic perturbation ⋮ An efficient numerical method for simulating the dynamics of coupling Bose-Einstein condensates in optical resonators ⋮ A determining form for the damped driven nonlinear Schrödinger equation -- Fourier modes case ⋮ Maximum norm error bound of a linearized difference scheme for a coupled nonlinear Schrödinger equations ⋮ Gauss-Seidel-type methods for energy states of a multi-component Bose-Einstein condensate ⋮ Comparisons between sine-Gordon and perturbed nonlinear Schrödinger equations for modeling light bullets beyond critical collapse ⋮ A finite difference continuation method for computing energy levels of Bose-Einstein condensates ⋮ Numerical studies on a novel split-step quadratic B-spline finite element method for the coupled Schrödinger-KdV equations ⋮ An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates ⋮ Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation ⋮ Global Well-Posedness for Cubic NLS with Nonlinear Damping ⋮ DYNAMICS OF THE GROUND STATE AND CENTRAL VORTEX STATES IN BOSE–EINSTEIN CONDENSATION ⋮ An accurate approximation of exponential integrators for the Schrödinger equation ⋮ Unnamed Item ⋮ Global attractor for damped forced nonlinear logarithmic Schrödinger equations ⋮ Spectral method and Bayesian parameter estimation for the space fractional coupled nonlinear Schrödinger equations ⋮ A continuation BSOR-Lanczos--Galerkin method for positive bound states of a multi-component Bose-Einstein condensate ⋮ Efficient dissipation-preserving approaches for the damped nonlinear Schrödinger equation ⋮ Optimal error estimates of explicit finite difference schemes for the coupled Gross–Pitaevskii equations
