Well-posedness of an integrable generalization of the nonlinear Schrödinger equation on the circle

DOI10.1007/s11005-011-0488-7zbMath1216.35136OpenAlexW2063262392MaRDI QIDQ539093

A. Alexandrou Himonas, Athanassios S. Fokas

Publication date: 27 May 2011

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-011-0488-7

zbMATH Keywords

Sobolev spacesenergy estimateswell-posednessnonlinear Schrödinger equationlifespanintegrable equationsperiodic Cauchy problemcontinuity of the data-to-solution map

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Methods of ordinary differential equations applied to PDEs (35A24) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (7)

The Fokas-Lenells equation on the line: global well-posedness with solitons ⋮ Well-posedness of the nonlinear Schrödinger equation on the half-plane ⋮ Long-time asymptotics for the focusing Fokas-Lenells equation in the solitonic region of space-time ⋮ The nonlinear Schrödinger equation on the half-line ⋮ Continuity properties of the solution map for the generalized reduced Ostrovsky equation ⋮ Then-order rogue waves of Fokas-Lenells equation ⋮ The periodic Cauchy problem for a two-component non-isospectral cubic Camassa-Holm system

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