The derivative NLS equation: global existence with solitons

TL;DR

This paper proves global existence for the derivative NLS equation with initial data containing solitons by employing Bäcklund transformations to simplify the associated Riemann--Hilbert problem.

Contribution

It introduces a novel application of Bäcklund transformations to handle initial data with solitons in the derivative NLS equation, extending previous global existence results.

Findings

Global existence established for derivative NLS with solitons

Bäcklund transformation simplifies the Riemann--Hilbert problem

Solvability of the transformed problem confirmed

Abstract

We extend the global existence result for the derivative NLS equation to the case when the initial datum includes a finite number of solitons. This is achieved by an application of the B\"acklund 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.