Global well-posedness for the derivative non-linear Schrödinger equation

DOI10.1080/03605302.2018.1475489zbMath1412.35309arXiv1710.03810OpenAlexW2900177971MaRDI QIDQ4626013

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Publication date: 26 February 2019

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.03810

zbMATH Keywords

soliton solutionsderivative nonlinear Schrödinger equationglobal well-posednessinverse scattering method

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) 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) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Uses Software

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Cites Work

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• Global well-posedness on the derivative nonlinear Schrödinger equation
• Global well-posedness for the derivative nonlinear Schrödinger equation in \(H^{\frac {1}{2}} (\mathbb{R})\)
• The semiclassical modified nonlinear Schrödinger equation I: Modulation theory and spectral analysis
• On the derivative nonlinear Schrödinger equation
• The derivative NLS equation: global existence with solitons
• Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data
• Matrix Riemann-Hilbert problems with jumps across Carleson contours
• Soliton resolution for the derivative nonlinear Schrödinger equation
• A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schrödinger equation
• Well-posedness for one-dimensional derivative nonlinear Schrödinger equations
• Riemann–Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions
• Global existence for the derivative nonlinear Schrödinger equation by the method of inverse scattering
• Scattering and inverse scattering for first order systems
• An exact solution for a derivative nonlinear Schrödinger equation
• Leading-order temporal asymptotics of the modified nonlinear Schrödinger equation: solitonless sector
• Long‐time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space
• Existence of Global Solutions to the Derivative NLS Equation with the Inverse Scattering Transform Method
• The Riemann–Hilbert Problem and Inverse Scattering
• The derivative nonlinear Schrödinger equation: Global well-posedness and soliton resolution
• The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases