Vortex clusters bifurcating from multipoles and second-order ring solitons

We address the existence, stability, and propagation dynamics of multipole solitons and vortex clusters in cubic-quintic media subject to a harmonic trapping potential. We found that vortex clusters comprising N off-centered vortices with alternating topological charges m=±1, evenly distributed on a ring, can bifurcate from a multipole soliton for N≤4 and from a second-order ring soliton for N>4. Rigorous linear stability analysis, corroborated by direct numerical simulations, shows that upper-branch vortex clusters with N=2 and 4 remain stable over a wide range of the propagation constant. Thus, we reveal the formation mechanism of vortex clusters.