Error propagation when approximating multi-solitons: The KdV equation as a case study
type: Item
instance of: scholarly article
title: Error propagation when approximating multi-solitons: The KdV equation as a case study
zbMATH Open document ID: 1203.65162
author: A. Durán
author: J. Álvarez
published in: Applied Mathematics and Computation
publication date: 2010-11-30T00:00:00Z
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 5821452
zbMATH Keywords: solitary waves
zbMATH Keywords: conservative numerical methods
zbMATH Keywords: geometric integration
zbMATH Keywords: multi-solitons
zbMATH Keywords: conserved quantities
zbMATH Keywords: numerical examples
zbMATH Keywords: error estimates
zbMATH Keywords: semidiscretization
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: Korteweg-de Vries (Kdv) equation
MaRDI profile type: Publication
full work available at URL: j.amc.2009.06.033
OpenAlex ID: W2051923885
cites work: Korteweg‐devries equation and generalizations. VI. methods for exact solution
cites work: The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
cites work: Integrals of nonlinear equations of evolution and solitary waves
cites work: The Korteweg–deVries Equation: A Survey of Results
cites work: Q4151274
cites work: Numerical schemes for a model for nonlinear dispersive waves
cites work: Collisions between two solitary waves. Part 2. A numerical study
cites work: Overtaking collision between two solitary waves
cites work: Accuracy and conservation properties in numerical integration: The case of the Korteweg-de Vries equation
cites work: Time behaviour of the error when simulating finite-band periodic waves. The case of the KdV equation
cites work: Completeness of Derivatives of Squared Schrödinger Eigenfunctions and Explicit Solutions of the Linearized K<scp>d</scp>V Equation
cites work: A Justification of the K<scp>d</scp>V Approximation to First Order in the Case ofN-Soliton Water Waves in a Canal
cites work: Inversion of the linearized Korteweg-de Vries equation at the multi-soliton solutions
cites work: Conserved quantities of some Hamiltonian wave equations after full discretization
cites work: Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part I
cites work: The numerical integration of relative equilibrium solutions. The nonlinear Schrodinger equation
cites work: Numerical behaviour of stable and unstable solitary waves
cites work: Asymptotic stability of solitary waves
cites work: Q4531870
cites work: Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
cites work: Theory of a Solid State Plasma Waveguide in a Transverse Magnetic Field
cites work: Reflectionless Transmission through Dielectrics and Scattering Potentials
cites work: On the stability of KdV multi‐solitons
cites work: The inverse scattering transform: Semi-infinite interval
cites work: Q3994822
cites work: A numerical and theoretical study of certain nonlinear wave phenomena
cites work: A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions
cites work: Stable and unstable solitary-wave solutions of the generalized regularized long-wave equation
cites work: Convergence of periodic wavetrains in the limit of large wavelength
cites work: Spectral Methods for a Nonlinear Initial Value Problem Involving Pseudo Differential Operators
cites work: A perfectly matched layer for the absorption of electromagnetic waves
cites work: Numerical simulation of a modified KdV equation on the whole real axis
cites work: Exact nonreflecting boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
cites work: Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
cites work: The generalized Dirichlet-to-Neumann map for certain nonlinear evolution PDEs
cites work: Invariants and numerical methods for ODEs
cites work: Q5719651
cites work: Q5558191
cites work: Q4403232
cites work: Solving Ordinary Differential Equations I
cites work: Asymptotic expansions of the global error of fixed-stepsize methods
cites work: Backward Error Analysis for Numerical Integrators
cites work: Q4945808
cites work: Backward error analysis for multi-symplectic integration methods
cites work: Backward error analysis for Lie-group methods
cites work: Error Growth in the Numerical Integration of Periodic Orbits, with Application to Hamiltonian and Reversible Systems
cites work: Solitary wave interactions of the Euler-Poisson equations
cites work: Eigenfunctions of Linearized Integrable Equations Expanded Around an Arbitrary Solution
cites work: A symmetry approach to exactly solvable evolution equations
cites work: Inverse scattering transform for the Camassa–Holm equation
cites work: Generalized Fourier transform for the Camassa–Holm hierarchy
cites work: Perturbation theory for the Benjamin-Ono equation
cites work: The existence of solitary waves

Error propagation when approximating multi-solitons: The KdV equation as a case study (cites work)
cites work: On the stability ofN-solitons in integrable systems

Error propagation when approximating multi-solitons: The KdV equation as a case study (DOI)
DOI: 10.1016/J.AMC.2009.06.033