Title: The derivative NLS equation: global existence with solitons,
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 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.