A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions
type: Item
instance of: scholarly article
title: A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions
zbMATH Open document ID: 1257.35165
author: Tamara Grava
author: C. Klein
published in: Physica D
publication date: 2013-01-30T00:00:00Z
full work available at URL: https://arxiv.org/abs/1202.0962
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 6132980
zbMATH Keywords: Korteweg
zbMATH Keywords: de Vries equation
zbMATH Keywords: dispersive shocks
zbMATH Keywords: multi-scale analysis
zbMATH Keywords: numerical methods
describes a project that uses: chebop
describes a project that uses: fminsearch
describes a project that uses: Matlab
MaRDI profile type: Publication
OpenAlex ID: W2077819267
arXiv ID: 1202.0962
cites work: On Hamiltonian perturbations of hyperbolic systems of conservation laws. II: Universality of critical behaviour
cites work: On universality of critical behaviour in Hamiltonian PDEs
cites work: On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation
cites work: The small dispersion limit of the Korteweg-de Vries equation. I
cites work: Q4339408
cites work: Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154)
cites work: Universality for the Focusing Nonlinear Schrödinger Equation at the Gradient Catastrophe Point: Rational Breathers and Poles of the Tritronquée Solution to Painlevé I
cites work: Universality in the Profile of the Semiclassical Limit Solutions to the Focusing Nonlinear Schrodinger Equation at the First Breaking Curve
cites work: Corrigenda to ``The sine-Gordon equation in the semiclassical limit: critical behavior near a separatrix''
cites work: Numerical Solution of the Small Dispersion Limit of the Camassa–Holm and Whitham Equations and Multiscale Expansions
cites work: Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg—de Vries equation in the small‐dispersion limit
cites work: Global well-posedness for KdV in Sobolev spaces of negative index
cites work: Semiclassical limit for generalized KdV equations before the gradient catastrophe
cites work: Q4151274
cites work: The korteweg-de vries equation with small dispersion: Higher order lax-levermore theory
cites work: Numerical solution of the small dispersion limit of Korteweg—de Vries and Whitham equations
cites work: Q3517523
cites work: Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach
cites work: Numerical study of a multiscale expansion of the Korteweg–de Vries equation and Painlevé-II equation
cites work: Solitonic Asymptotics for the Korteweg–de Vries Equation in the Small Dispersion Limit
cites work: Q5394330
cites work: Orthogonal polynomials and random matrices: a Riemann-Hilbert approach.
cites work: Q4487945
cites work: The isomonodromy approach to matrix models in 2D quantum gravity
cites work: Painlevé I asymptotics for orthogonal polynomials with respect to a varying quartic weight
cites work: Double scaling limit in the random matrix model: The Riemann-Hilbert approach
cites work: Universality of the double scaling limit in random matrix models
cites work: Multi-critical unitary random matrix ensembles and the general Painlevé II equation
cites work: First colonization of a hard-edge in random matrix theory
cites work: Birth of a Cut in Unitary Random Matrix Ensembles
cites work: The Riemann-Hilbert Approach to Double Scaling Limit of Random Matrix Eigenvalues Near the "Birth of a Cut" Transition
cites work: Universal distribution of random matrix eigenvalues near the ‘birth of a cut’ transition
cites work: Universality of a double scaling limit near singular edge points in random matrix models
cites work: The initial value problem for the Whitham averaged system
cites work: Q3743738
cites work: Oscillations of the zero dispersion limit of the korteweg‐de vries equation
cites work: The existence of a real pole-free solution of the fourth order analogue of the Painlevé I equation
cites work: The KdV Hierarchy: Universality and a Painlevé Transcendent
cites work: A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation
cites work: The generation, propagation, and extinction of multiphases in the KdV zero-dispersion limit
cites work: Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
cites work: Fourth order time-stepping for low dispersion Korteweg-de Vries and nonlinear Schrödinger equations
cites work: Q3262547
cites work: Exponential integrators
cites work: Exponential time differencing for stiff systems
cites work: Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
cites work: A Practical Guide to Pseudospectral Methods
cites work: Barycentric Lagrange Interpolation
cites work: Spectral Methods in MATLAB
cites work: The chebop system for automatic solution of differential equations
cites work: Numerical solution of Riemann-Hilbert problems: Painlevé II
cites work: On the numerical evaluation of Fredholm determinants
cites work: A numerical methodology for the Painlevé equations
cites work: Numerical Study of Breakup in Generalized Korteweg–de Vries and Kawahara Equations
cites work: Asymptotics for a special solution to the second member of the Painlevé I hierarchy
cites work: Phase shift in the Whitham zone for the Gurevich-Pitaevskii special solution of the Korteweg-de Vries equation

A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions (DOI)
DOI: 10.1016/J.PHYSD.2012.04.001