We present a comprehensive theoretical investigation of the formation and propagation of multicolor ringlike soliton clusters in quadratic nonlinear materials under conditions for type I second-harmonic generation. We show the several existing propagation regimes for the soliton clusters, which include fusion, expansion, and quasi-stationary propagation. The physical mechanism that leads to each evolution is elucidated and discussed. In the case of purely expanding clusters, accurate estimates of the expansion rate are obtained with a Hamiltonian approach. The experimental formation of the different soliton clusters by induced breakup techniques is discussed in detail, and the practical limitations of the concept of quasi-stationary clusters are highlighted.
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