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Global existence for
the derivative nonlinear Schrödinger equation with arbitrary
spectral singularities
Robert Jenkins, Jiaqi Liu, Peter Perry and Catherine Sulem |
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Vol. 13 (2020), No. 5, 1539–1578
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Abstract |
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We show that the derivative nonlinear Schrödinger (DNLS) equation is globally well-posed in the weighted Sobolev space . Our result exploits the complete integrability of the DNLS equation and removes certain spectral conditions on the initial data required by our previous work, thanks to Zhou’s analysis (Comm. Pure Appl. Math. 42:7 (1989), 895–938) on spectral singularities in the context of inverse scattering. |
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Keywords
derivative nonlinear Schrödinger, inverse scattering,
global well-posedness
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Mathematical Subject Classification 2010
Primary: 35Q55, 37K15
Secondary: 35P25, 35R30
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Milestones
Received: 5 September 2018
Revised: 16 April 2019
Accepted: 31 May 2019
Published: 27 July 2020
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Authors |
| Robert Jenkins | |
| Department of Mathematics Colorado State University Fort Collins, CO United States |
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| Jiaqi Liu | |
| Department of Mathematics University of Toronto Toronto, ON Canada |
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| Peter Perry | |
| Department of Mathematics University of Kentucky Lexington, KY United States |
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| Catherine Sulem | |
| Department of Mathematics University of Toronto Toronto, ON Canada |
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