  We consider a derivative nonlinear Schr{\"o}dinger equation with general
nonlinearlity: i$\partial$tu + $\partial$ 2 x u + i|u| 2$\sigma$ $\partial$xu =
0, In [12], the authors prove the stability of two solitary waves in energy
space for $\sigma$ $\in$ (1, 2). As a consequence, there exists a two-soliton
trains in energy space for $\sigma$ $\in$ (1, 2). Our goal in this paper is
proving the existence of multi-soliton trains in energy space for $\sigma$ 5 2.
Our proofs proceed by xed point arguments around the desired prole, using
Strichartz estimates.
