Stability of the traveling waves for the derivative Schr\"odinger equation in the energy space

In this paper, we continue the study of the dynamics of the traveling waves for nonlinear Schr\"odinger equation with derivative (DNLS) in the energy space. Under some technical assumptions on the speed of each traveling wave, the stability of the sum of two traveling waves for DNLS is obtained in the energy space by Martel-Merle-Tsai's analytic approach in \cite{MartelMT:Stab:gKdV, MartelMT:Stab:NLS}. As a by-product, we also give an alternative proof of the stability of the single traveling wave in the energy space in \cite{ColinOhta-DNLS}, where Colin and Ohta made use of the concentration-compactness argument.