scientific article; zbMATH DE number 714428

Stephanos Venakides, Peter D. Lax, C. David Levermore

Publication date: 24 August 1995

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Korteweg-de Vries equation nonlinear Schrödinger equations inverse scattering method fluid dynamics Hopf equations dispersive processes

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (37)

The behavior of the Weyl function in the zero-dispersion KdV limit ⋮ The generation, propagation, and extinction of multiphases in the KdV zero-dispersion limit ⋮ Advection of passive and reactive tracers in multi-dimensional Burgers' velocity field ⋮ Quasicontinuum models of dynamic phase transitions ⋮ Modulation of multiphase waves in the presence of resonance ⋮ On Hamiltonian perturbations of hyperbolic systems of conservation laws. II: Universality of critical behaviour ⋮ Single-phase averaging for the Ablowitz-Ladik chain ⋮ Approximation of functional compact sets by analytic varieties ⋮ Damped-driven KdV and effective equations for long-time behaviour of its solutions ⋮ Multi-phase computations of the semiclassical limit of the Schrödinger equation and related problems: Whitham vs Wigner ⋮ Convergence of difference schemes with high resolution for conservation laws ⋮ Binary modulated oscillations in a semi-discrete version of Burgers equation ⋮ The whitham equations revisited ⋮ Finite genus solutions to the Ablowitz‐Ladik equations ⋮ Generating function of the Whitham-KdV hierarchy and effective solution of the Cauchy problem. ⋮ Finite gap conditions and small dispersion asymptotics for the classical periodic Benjamin–Ono equation ⋮ Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory ⋮ Some survey remarks on Whitham theory and Em duality ⋮ Whitham equations and phase shifts for the Korteweg–de Vries equation ⋮ Central Discontinuous Galerkin Methods for the Generalized Korteweg-de Vries Equation ⋮ Numerical experiments on the modulation theory for the nonlinear atomic chain ⋮ Dispersive shock waves and modulation theory ⋮ Small dispersion limit of the Korteweg-de Vries equation with periodic initial conditions and analytical description of the Zabusky-Kruskal experiment ⋮ Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert problem approach ⋮ Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical lattices ⋮ Decay of an initial discontinuity in the defocusing NLS hydrodynamics ⋮ Existence and modulation of traveling waves in particles chains ⋮ The semiclassical limit of the defocusing NLS hierarchy ⋮ Initial value problem of the Whitham equations for the Camassa-Holm equation ⋮ Binary and ternary oscillations in a cubic numerical scheme ⋮ On dispersive difference schemes ⋮ On formal solutions to matrix version of a reduced Kac--van Moerbeke equation ⋮ Large oscillations arising in a dispersive numerical scheme ⋮ Riemann–Hilbert problem to the modified Korteveg–de Vries equation: Long-time dynamics of the steplike initial data ⋮ A numerical study of the perturbed semiclassical focusing nonlinear Schrödinger equation ⋮ Dynamics of counterpropagating waves in parametrically driven systems: dispersion vs. advection ⋮ On critical behaviour in systems of Hamiltonian partial differential equations

This page was built for publication: