  In this paper, we show the orbital stability of solitons arising in the cubic
derivative nonlinear Schrodinger equations. We consider the zero mass case that
is not covered by earlier works [8, 3]. As this case enjoys L^2 scaling
invariance, we expect the orbital stability in the sense up to scaling
symmetry, in addition to spatial and phase translations. For the proof, we are
based on the variational argument and extend a similar argument in [21].
Moreover, we also show a self-similar type blow up criteria of solutions with
the critical mass 4{\pi}.
