Exponential integrators for nonlinear Schrödinger equations with white noise dispersion

DOI10.1007/s40072-017-0098-1zbMath1386.65036OpenAlexW2599234101WikidataQ59603552 ScholiaQ59603552MaRDI QIDQ1706673

Peng Zhang

Publication date: 28 March 2018

Published in: Stochastic and Partial Differential Equations. Analysis and Computations (Search for Journal in Brave)

Full work available at URL: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-137244

zbMATH Keywords

numerical methodsstochastic partial differential equationsnonlinear Schrödinger equationmean-square convergenceexponential integratorsgeometric numerical integrationwhite noise dispersion

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (10)

Strong Rates of Convergence of a Splitting Scheme for Schrödinger Equations with Nonlocal Interaction Cubic Nonlinearity and White Noise Dispersion ⋮ Approximated exponential integrators for the stochastic Manakov equation ⋮ Data-driven structure-preserving model reduction for stochastic Hamiltonian systems ⋮ An explicit exponential integrator based on Faber polynomials and its application to seismic wave modeling ⋮ Strong convergence rate of splitting schemes for stochastic nonlinear Schrödinger equations ⋮ Numerical Analysis of the Midpoint Scheme for the Generalized Benjamin-Bona-Mahony Equation with White Noise Dispersion ⋮ Lie-Trotter splitting for the nonlinear stochastic Manakov system ⋮ Multirevolution Integrators for Differential Equations with Fast Stochastic Oscillations ⋮ A splitting/polynomial chaos expansion approach for stochastic evolution equations ⋮ Exponential integrators for stochastic Maxwell's equations driven by Itô noise

Cites Work

• An exponential integrator scheme for time discretization of nonlinear stochastic wave equation
• The numerical approximation of stochastic partial differential equations
• 1D quintic nonlinear Schrödinger equation with white noise dispersion
• One-stage exponential integrators for nonlinear Schrödinger equations over long times
• On a splitting scheme for the nonlinear Schrödinger equation in a random medium
• Symmetric exponential integrators with an application to the cubic Schrödinger equation
• The nonlinear Schrödinger equation with white noise dispersion
• Conservation of phase space properties using exponential integrators on the cubic Schrödinger equation
• Exponential Runge-Kutta methods for the Schrödinger equation
• Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion
• Exponential integrators for quantum-classical molecular dynamics
• Exponential time integration of solitary waves of cubic Schrödinger equation
• Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion
• A fully discrete approximation of the one-dimensional stochastic wave equation
• Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise
• Exponential integrators
• A numerical scheme for stochastic PDEs with Gevrey regularity
• Exponential Integrators for Stochastic Schrödinger Equations Driven by Itô Noise
• A Trigonometric Method for the Linear Stochastic Wave Equation
• Stochastic exponential integrators for the finite element discretization of SPDEs for multiplicative and additive noise
• Projected explicit lawson methods for the integration of Schrödinger equation
• High Order Exponential Integrators for Nonlinear Schrödinger Equations with Application to Rotating Bose--Einstein Condensates
• Probability and Pathwise Order of Convergence of a Semidiscrete Scheme for the Stochastic Manakov Equation
• Geometric Numerical Integration

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