An Embedded Exponential-Type Low-Regularity Integrator for mKdV Equation
DOI10.1137/21M1408166OpenAlexW4280518394WikidataQ115525515 ScholiaQ115525515MaRDI QIDQ5080496
No author found.
Publication date: 31 May 2022
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/21m1408166
error estimatemKdV equationMiura transformrough dataexponential-type integratoriterative regularizing
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Analytical and numerical aspects of certain nonlinear evolution equations. I. Analytical
- Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation
- Fourth order time-stepping for low dispersion Korteweg-de Vries and nonlinear Schrödinger equations
- Global wellposedness of KdV in \(H^{-1}(\mathbb T,\mathbb R)\)
- Numerical simulation of a modified KdV equation on the whole real axis
- Two remarks on the generalised Korteweg de-Vries equation
- Analytical and numerical aspects of certain nonlinear evolution equations. IV: Numerical, modified Korteweg-de Vries equation
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
- Approximation of the Korteweg-de Vries equation by the nonlinear Schrödinger equation
- Operator splitting methods for generalized Korteweg-de Vries equations
- The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
- Low regularity exponential-type integrators for semilinear Schrödinger equations
- On Kato-Ponce and fractional Leibniz
- Multilinear estimates for periodic KdV equations, and applications
- Rough solutions for the periodic Korteweg-de Vries equation
- Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity
- Embedded exponential-type low-regularity integrators for KdV equation under rough data
- A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation
- Two exponential-type integrators for the ``good Boussinesq equation
- On an endpoint Kato-Ponce inequality.
- An exponential-type integrator for the KdV equation
- A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect
- A numerical application of the decomposition method for the combined KdV-MKdV equation
- On spectral approximations using modified Legendre rational functions: Application to the Korteweg-de Vries equation on the half line
- Conservative, discontinuous Galerkin–methods for the generalized Korteweg–de Vries equation
- Exponential integrators
- Spectral Methods
- On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
- Operator splitting for the KdV equation
- Commutation Methods Applied to the mKdV-Equation
- Convergence of an Embedded Exponential-Type Low-Regularity Integrators for the KdV Equation without Loss of Regularity
- Fully discrete galerkin methods for the korteweg-de vries equation
- Error analysis for spectral approximation of the Korteweg-de Vries equation
- Commutator estimates and the euler and navier-stokes equations
- A New Dual-Petrov-Galerkin Method for Third and Higher Odd-Order Differential Equations: Application to the KDV Equation
- Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
- NUMERICAL SIMULATION OF THE KdV-MKdV EQUATION
- Spectral Methods in MATLAB
- Optimal Error Estimates of the Legendre--Petrov--Galerkin Method for the Korteweg--de Vries Equation
- Global well-posedness for periodic generalized Korteweg-de Vries equation
- Accelerating the Nonuniform Fast Fourier Transform
- Global Well-Posedness of mKdV inL2(𝕋, ℝ)
- Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
- A Local Discontinuous Galerkin Method for KdV Type Equations
- Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
- Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation
- Operator splitting for partial differential equations with Burgers nonlinearity
- A General Framework of Low Regularity Integrators
- Error estimates at low regularity of splitting schemes for NLS
- Resonance-based schemes for dispersive equations via decorated trees
- Optimal convergence of a second-order low-regularity integrator for the KdV equation
- A first-order Fourier integrator for the nonlinear Schrödinger equation on 𝕋 without loss of regularity
- Low-regularity integrators for nonlinear Dirac equations
- A posteriori error estimates for discontinuous Galerkin methods for the generalized Korteweg-de Vries equation
- On Optimal High-Order in Time Approximations for the Korteweg-De Vries Equation
- A Fourier Integrator for the Cubic Nonlinear Schrödinger Equation with Rough Initial Data
- Error estimates of finite difference schemes for the Korteweg–de Vries equation
- A Lawson-type exponential integrator for the Korteweg–de Vries equation
- Weakly nonlinear wavepackets in the Korteweg-de Vries equation: The KdV/NLS connection