  We present a generalized study and characterization of the integrability
properties of the derivative non-linear Schr\"odinger equation in 1+1
dimensions. A Lax pair is derived for this equation by means of a Miura
transformation and the singular manifold method. This procedure, together with
the Darboux transformations, allow us to construct a wide class of rational
soliton-like solutions. Lie classical symmetries have also been computed and
similarity reductions have been analyzed and discussed.
