Vortex clusters bifurcating from multipoles and second-order ring solitons
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Updated: Sep 25, 2026

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Abstract:
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.
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