On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data

DOI10.1090/jams/837zbMath1342.35300arXiv1212.2674OpenAlexW2963691387MaRDI QIDQ2802072

David Damanik, Michael Goldstein

Publication date: 25 April 2016

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.2674

zbMATH Keywords

KdV equationexistence and uniquenessDiophantine frequencyexponentially decaying Fourier coefficientsquasi-periodic initial data

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) Almost and pseudo-almost periodic solutions to PDEs (35B15)

Related Items (18)

Almost periodicity in time of solutions of the KdV equation ⋮ Solution of the Korteweg-de Vries equation on the line with analytic initial potential ⋮ Exponential upper bounds on the spectral gaps and homogeneous spectrum for the non-critical extended Harper's model ⋮ Space quasi-periodic standing waves for nonlinear Schrödinger equations ⋮ Construction of KdV flow: a unified approach ⋮ The nonlinear Schrödinger equation on Z and R with bounded initial data: examples and conjectures ⋮ Global well-posedness for \(H^{-1}(\mathbb{R})\) perturbations of KdV with exotic spatial asymptotics ⋮ The quasi-periodic Cauchy problem for the generalized Benjamin-Bona-Mahony equation on the real line ⋮ Uniform Estimate of Potentials by Reflection Coefficients and its Application to KdV Flow ⋮ Mini-workshop: Reflectionless operators: the Deift and Simon conjectures. Abstracts from the mini-workshop held October 22--28, 2017 ⋮ The isospectral torus of quasi-periodic Schrödinger operators via periodic approximations ⋮ Some open problems in random matrix theory and the theory of integrable systems. II ⋮ Invariance of white noise for KdV on the line ⋮ Uniqueness of solutions of the KdV-hierarchy via Dubrovin-type flows ⋮ Semi-algebraic sets method in PDE and mathematical physics ⋮ On Nonlinear Schrödinger Equations with Almost Periodic Initial Data ⋮ Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in L p-based Sobolev spaces ⋮ Global existence for the defocusing nonlinear Schrödinger equations with limit periodic initial data

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