Adiabatic midpoint rule for the dispersion-managed nonlinear Schrödinger equation
DOI10.1007/s00211-017-0926-2zbMath1448.65107OpenAlexW2767935848MaRDI QIDQ1742494
Publication date: 11 April 2018
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://publikationen.bibliothek.kit.edu/1000060572
Asymptotic behavior of solutions to PDEs (35B40) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs with low regular coefficients and/or low regular data (35R05) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Applications to the sciences (65Z05)
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Cites Work
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- Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime
- Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation
- Geometric numerical integration and Schrödinger equations
- Numerical stroboscopic averaging for ODEs and DAEs
- High-order splitting schemes for semilinear evolution equations
- Decay estimates and smoothness for solutions of the dispersion managed non-linear Schrödinger equation
- Splitting integrators for nonlinear Schrödinger equations over long times
- Numerical integrators for quantum dynamics close to the adiabatic limit
- A Gautschi-type method for oscillatory second-order differential equations
- Stroboscopic averaging for the nonlinear Schrödinger equation
- Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations
- Adiabatic integrators for highly oscillatory second-order linear differential equations with time-varying eigendecomposition
- Exponential decay of dispersion-managed solitons for general dispersion profiles
- PLANE WAVE STABILITY OF THE SPLIT-STEP FOURIER METHOD FOR THE NONLINEAR SCHRÖDINGER EQUATION
- Exponential integrators
- On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
- The heterogeneous multiscale method
- Computing Semiclassical Quantum Dynamics with Hagedorn Wavepackets
- Long-Time-Step Methods for Oscillatory Differential Equations
- Averaging of Dispersion-Managed Solitons: Existence and Stability
- Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting
- Long-Time-Step Integrators for Almost-Adiabatic Quantum Dynamics
- Structure-Preserving Algorithms for Oscillatory Differential Equations
- Error Analysis of Trigonometric Integrators for Semilinear Wave Equations
- Numerical Integrators for Highly Oscillatory Hamiltonian Systems: A Review
- Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential
- Error analysis of exponential integrators for oscillatory second-order differential equations
- Geometric Numerical Integration
- On the Construction and Comparison of Difference Schemes
- Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations
- Functional analysis
- Stabilizing effects of dispersion management
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