The Korteweg–de Vries equation on the half-line

DOI10.1088/0951-7715/29/2/489zbMath1335.35216OpenAlexW2512502655MaRDI QIDQ2794861

A. Alexandrou Himonas, Athanassios S. Fokas, Dionyssios Mantzavinos

Publication date: 11 March 2016

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/29/2/489

zbMATH Keywords

Laplace transforminitial-boundary value problemKorteweg-de Vries equationbilinear estimateswell-posedness in Sobolev spacesunified transform methodintegrable equation with solitons

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) A priori estimates in context of PDEs (35B45) Laplace transform (44A10) Initial-boundary value problems for linear higher-order PDEs (35G16) Initial-boundary value problems for nonlinear higher-order PDEs (35G31)

Related Items (29)

Airy-type evolution equations on star graphs ⋮ The Korteweg-de Vries equation on the half-line with Robin and Neumann data in low regularity spaces ⋮ A higher dispersion KdV equation on the half-line ⋮ Well-posedness and nonlinear smoothing for the ``good Boussinesq equation on the half-line ⋮ Sharp well-posedness of the biharmonic Schrödinger equation in a quarter plane ⋮ Asymptotic Stability of KdV Solitons on the Half-Line: A Study in the Energy Space ⋮ Boundary behavior for the heat equation on the half‐line ⋮ The Majda-Biello system on the half-line ⋮ The linear Lugiato-Lefever equation with forcing and nonzero periodic or nonperiodic boundary conditions ⋮ Boundary behavior of the solution to the linear Korteweg‐De Vries equation on the half line ⋮ Low regularity well-posedness for dispersive equations on semi-infinite intervals ⋮ The Korteweg-de Vries equation on an interval ⋮ Well-posedness of the nonlinear Schrödinger equation on the half-plane ⋮ Sharp well-posedness for the generalized KdV of order three on the half line ⋮ \(N\)-soliton solutions for the nonlocal Fokas-Lenells equation via RHP ⋮ Well-posedness of a higher dispersion KdV equation on the half-line ⋮ Lower regularity solutions of the biharmonic Schrödinger equation in a quarter plane ⋮ The nonlinear Schrödinger equation on the half-line with a Robin boundary condition ⋮ The nonlinear Schrödinger equation on the half-line with Neumann boundary conditions ⋮ Well-posedness and lower bounds of the growth of weighted norms for the Schrödinger-Korteweg-de Vries interactions on the half-line ⋮ Initial boundary value problems for some nonlinear dispersive models on the half-line: a review and open problems ⋮ Stability of KdV solitons on the half-line ⋮ Qualitative analysis of the dynamic for the nonlinear Korteweg-de Vries equation with a boundary memory ⋮ Local regularity properties for 1D mixed nonlinear Schrödinger equations on half-line ⋮ Non-homogeneous boundary value problems of the fifth-order KdV equations on a bounded interval ⋮ The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line ⋮ Evolution partial differential equations with discontinuous data ⋮ Initial-boundary value problems for a reaction-diffusion equation ⋮ The Neumann and Robin problems for the Korteweg–de Vries equation on the half-line

This page was built for publication: The Korteweg–de Vries equation on the half-line