Vortex equation and reflexive sheaves

It is known that given a stable holomorphic pair $(E,\varphi )$, where $E$ is a holomorphic vector bundle on a compact K"ahler manifold $X$ and $\varphi$ is a holomorphic section of $E$, the vector bundle $E$ admits a Hermitian metric solving the vortex equation. We generalize this to pairs $(\text{E},\varphi )$, where $\text{E}$ is a reflexive sheaf on $X$.