Dynamics of Partial Differential Equations
Volume 14 (2017)
The derivative NLS equation: global existence with solitons
Pages: 271 – 294
We prove the global existence result for the derivative NLS equation in the case when the initial datum includes a finite number of solitons. This is achieved by an application of the Bäcklund transformation that removes a finite number of zeros of the scattering coefficient. By means of this transformation, the Riemann–Hilbert problem for meromorphic functions can be formulated as the one for analytic functions, the solvability of which was obtained recently. A major difficulty in the proof is to show invertibility of the Bäcklund transformation acting on weighted Sobolev spaces.
derivative nonlinear Schrödinger equation, global existence, Bäcklund transformation, inverse scattering transform, solitons
2010 Mathematics Subject Classification
35P25, 35Q55, 37K40
A.S. gratefully acknowledges financial support from the projects “Quantum Matter and Materials” and SFB-TRR 191 “Symplectic Structures in Geometry, Algebra and Dynamics” (Cologne University, Germany).
Received 31 May 2017
Published 8 September 2017