We develop inverse scattering for the derivative nonlinear Schrödinger equation (DNLS) on the line using its gauge equivalence with a related nonlinear dispersive equation. We prove Lipschitz continuity of the direct and inverse scattering maps from the weighted Sobolev spaces H2,2(ℝ) to itself. These results immediately imply global existence of solutions to the DNLS for initial data in a spectrally determined (open) subset of H2,2(ℝ) containing a neighborhood of 0. Our work draws ideas from the pioneering work of Lee and from more recent work of Deift and Zhou on the nonlinear Schrödinger equation.
|Number of pages||69|
|Journal||Communications in Partial Differential Equations|
|State||Published - Nov 1 2016|
Bibliographical notePublisher Copyright:
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- Derivative nonlinear Schrodinger equation
- global well-posedness
- inverse scattering method
- solitonless solutions
ASJC Scopus subject areas
- Applied Mathematics