  We implement the dressing method for a novel integrable generalization of the
nonlinear Schr\"odinger equation. As an application, explicit formulas for the
$N$-soliton solutions are derived. As a by-product of the analysis, we find a
simplification of the formulas for the $N$-solitons of the derivative nonlinear
Schr\"odinger equation given by Huang and Chen.
