The derivative nonlinear Schrödinger equation: Global well-posedness and soliton resolution

DOI10.1090/qam/1553zbMath1434.35180arXiv1905.02866OpenAlexW2974570919MaRDI QIDQ4972698

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Publication date: 26 November 2019

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.02866

zbMATH Keywords

nonlinear Schrödinger equationsolitonglobal wellposednesssoliton resolution conjecture

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Global well-posedness for the derivative nonlinear Schrödinger equation ⋮ A robust way to justify the derivative NLS approximation ⋮ Optimal small data scattering for the generalized derivative nonlinear Schrödinger equations ⋮ On the well-posedness problem for the derivative nonlinear Schrödinger equation ⋮ Global well-posedness for the derivative non-linear Schrödinger equation ⋮ On a class of solutions to the generalized derivative Schrödinger equations. II ⋮ Long-time asymptotic behavior of a mixed Schrödinger equation with weighted Sobolev initial data ⋮ Optimal local well-posedness for the periodic derivative nonlinear Schrödinger equation ⋮ Remarks on blow-up criteria for the derivative nonlinear Schrödinger equation under the optimal threshold setting ⋮ Microscopic conservation laws for the derivative nonlinear Schrödinger equation

Uses Software

• DLMF

Cites Work

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