  The present work addresses the study and characterization of the
integrability of three famous nonlinear Schr\"odinger equations with
derivative-type nonlinearities in 1+1 dimensions. Lax pairs for these three
equations are successfully obtained by means of a Miura transformation and the
singular manifold method. After implementing the associated binary Darboux
transformations, we are able to construct rational soliton-like solutions for
those systems.
