Global existence for the derivative NLS equation in the presence of solitons

Abstract

We prove the existence of global solutions to the DNLS equation with initial data in a large subset of $H^2(\mathbb{R})\cap H^{1,1}(\mathbb{R})$ containing a neighborhood of all solitons. We use the inverse scattering transform method, which was recently developed by D. Pelinovsky and Y. Shimabukuro, and an auto-Bäcklund transform in order to include solitons.

26 pages

References in corpus (1)

• Global Well-posedness and soliton resolution for the Derivative Nonlinear Schrödinger equation

Cited by in corpus (2)

• On the well-posedness problem for the derivative nonlinear Schrödinger equation
• Long-time asymptotics for the Massive Thirring model