$SO(4)$ gauged $O(5)$ Skyrmion on $\mathbb{R}^4$

We have studied an $SO(4)$ gauged $O(5)$ Skyrmion on $\mathbb{R}^4$ which can be seen as a static soliton in $4+1$ dimensions. This is a sequel of the known $SO(D)$ gauged $O(D+1)$ Skyrmions on $\mathbb{R}^D$ in $D=2$ and in $D=3$, like which they are localised to an absolute scale and are topologically stable, their energies being bounded below by the winding number. In the absence of an analytic proof of existence some such solutions are constructed numerically. Two families of solutions are found, of which only one possesses a gauge decoupling limit. The curvatures of both of these solutions decay as $r^{-3}$, a property they share with the Yang-Mills instantons on $\mathbb{R}^4$.