Stability of the sum of two solitary waves for (gDNLS) in the energy space

In this paper, we continue the study in 18]. We use the perturbation argument, modulational analysis and the energy argument in 15], 16] to show the stability of the sum of two solitary waves with weak interactions for the generalized derivative Schrödinger equation (gDNLS) in the energy space. Here (gDNLS) hasn't the Galilean transformation invariance, the pseudo-conformal invariance and the gauge transformation invariance, and the case $\sigma >1$ we considered corresponds to the $L^2$-supercritical case.