Lie-Trotter operator splitting spectral method for linear semiclassical fractional Schrödinger equation
DOI10.1016/j.camwa.2022.03.016zbMath1504.65227OpenAlexW4293254935WikidataQ114201477 ScholiaQ114201477MaRDI QIDQ2122636
Publication date: 7 April 2022
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2022.03.016
error estimatesa priori estimatessemiclassical regimespectral methodsfractional Schrödinger equationLie-Trotter operator splitting
Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11) Numerical solutions to abstract evolution equations (65J08)
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Cites Work
- Unnamed Item
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- Fast alternating-direction finite difference methods for three-dimensional space-fractional diffusion equations
- An energy conservative difference scheme for the nonlinear fractional Schrödinger equations
- Crank-Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative
- Effective approximation for the semiclassical Schrödinger equation
- Hitchhiker's guide to the fractional Sobolev spaces
- Galerkin finite element method for nonlinear fractional Schrödinger equations
- Local elliptic regularity for the Dirichlet fractional Laplacian
- A fourth-order implicit-explicit scheme for the space fractional nonlinear Schrödinger equations
- An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime
- Geometric numerical integration and Schrödinger equations
- Fractional derivatives for physicists and engineers. Volume I: Background and theory. Volume II: Applications
- The Pohozaev identity for the fractional Laplacian
- Generalized Taylor's formula
- From quantum to classical molecular dynamics: Reduced models and numerical analysis.
- Well-posedness for semi-relativistic Hartree equations of critical type
- Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit
- On a Riemann-Liouville generalized Taylor's formula
- Fractional quantum mechanics and Lévy path integrals
- On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
- On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions
- The locally extrapolated exponential splitting scheme for multi-dimensional nonlinear space-fractional Schrödinger equations
- On the continuum limit for discrete NLS with long-range lattice interactions
- Efficient exponential splitting spectral methods for linear Schrödinger equation in the semiclassical regime
- Fractional Schrödinger dynamics and decoherence
- Fourier pseudospectral method on generalized sparse grids for the space-fractional Schrödinger equation
- Lump, mixed lump-stripe and rogue wave-stripe solutions of a \((3+1)\)-dimensional nonlinear wave equation for a liquid with gas bubbles
- Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation
- Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma
- Shallow water in an open sea or a wide channel: auto- and non-auto-Bäcklund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system
- Water-wave symbolic computation for the Earth, Enceladus and Titan: the higher-order Boussinesq-Burgers system, auto- and non-auto-Bäcklund transformations
- A conservative difference scheme for solving the strongly coupled nonlinear fractional Schrödinger equations
- Hetero-Bäcklund transformation and similarity reduction of an extended (2+1)-dimensional coupled Burgers system in fluid mechanics
- What is the fractional Laplacian? A comparative review with new results
- Vector bright solitons and their interactions of the couple Fokas-Lenells system in a birefringent optical fiber
- Error analysis and numerical simulations of Strang splitting method for space fractional nonlinear Schrödinger equation
- A numerical method for the fractional Schrödinger type equation of spatial dimension two
- The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
- Boson stars as solitary waves
- Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results
- Existence and stability of standing waves for nonlinear fractional Schrödinger equations
- Soliton dynamics for fractional Schrödinger equations
- Spectral Methods
- Mathematical and computational methods for semiclassical Schrödinger equations
- Operator splitting for the KdV equation
- Splitting methods
- Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
- The Lie-Trotter splitting for nonlinear evolutionary problems with critical parameters: a compact local error representation and application to nonlinear Schrodinger equations in the semiclassical regime
- Analysis and Approximation of a Fractional Cahn--Hilliard Equation
- On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross–Pitaevskii equations
- Lax pair, binary Darboux transformations and dark-soliton interaction of a fifth-order defocusing nonlinear Schrödinger equation for the attosecond pulses in the optical fiber communication
- A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
- Numerical study of fractional nonlinear Schrödinger equations
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