We study the derivative nonlinear Schrödinger (DNLS) equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but exclude spectral singularities). We show that the set of such initial data is open and dense in a weighted Sobolev space, and includes data of arbitrarily large L 2 -norm. We prove global well-posedness on this open and dense set. In a subsequent paper, we will use these results and a steepest descent analysis to prove the soliton resolution conjecture for the DNLS equation with the initial data considered here and asymptotic stability of N-soliton solutions.
|Number of pages||45|
|Journal||Communications in Partial Differential Equations|
|State||Published - Aug 3 2018|
Bibliographical noteFunding Information:
PAP was supported in part by NSF Grant DMS-1208778 and by Simons Foundation Research and Travel Grant 359431, and CS was supported in part by Grant 46179-13 from the Natural Sciences and Engineering Research Council of Canada.
© 2018, © 2018 Taylor & Francis.
- Derivative nonlinear Schrödinger equation
- global well-posedness
- inverse scattering method
- soliton solutions
ASJC Scopus subject areas
- Applied Mathematics