Abstract
We show that the derivative nonlinear Schrodinger (DNLS) equation is globally well-posed in the weighted Sobolev space H2,2(R). 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.
| Original language | English |
|---|---|
| Pages (from-to) | 1539-1578 |
| Number of pages | 40 |
| Journal | Analysis and PDE |
| Volume | 13 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Funding Information:We thank Deniz Bilman and Peter Miller for helpful discussions on Zhou's ideas. This work was supported by a grant from the Simons Foundation/SFARI (359431, PAP). CS is supported in part by Discovery Grant 2018-04536 from the Natural Sciences and Engineering Research Council of Canada.
Funding Information:
We thank Deniz Bilman and Peter Miller for helpful discussions on Zhou’s ideas. This work was supported by a grant from the Simons Foundation/SFARI (359431, PAP). CS is supported in part by Discovery Grant 2018-04536 from the Natural Sciences and Engineering Research Council of Canada.
Publisher Copyright:
© 2020 Mathematical Sciences Publishers.
Keywords
- Derivative nonlinear schrödinger
- Global well-posedness
- Inverse scattering
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Applied Mathematics