The derivative NLS equation: global existence with solitons

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.