Description of the simulations :
Bound state configurations of $N_v$ vortices found in high-precision large-scale numerical minimization of the three-component Ginzburg-Landau free energy in the type-II regime. The variational problem is defined using a finite element formulation provided by Freefem++ library. A nonlinear conjugate gradient algorithm is used to find the minima of the energy. More details about the numerical methods employed to study can be found in a Supplementary Material Letter .

The movies show the numerical evolution of the system, during the relaxation. Although not solving the Time Dependent Ginzburg-Landau equation (TDGL), numerical evolution reflects the structure of the free energy landscape of the system. And thus provides a qualitative insight of the possible dynamical mechanisms leading to the soliton formation.

The displayed quantities: From left to right, on the first line are plotted the total energy density $E_t$, and the `self induced phase differences' $~\mathrm{Im}(\psi_1^*\psi_2)$ and $~\mathrm{Im}(\psi_1^*\psi_3)$. The third phase difference $~\mathrm{Im}(\psi_2^*\psi_3)$ can be obtained from the informations of the two first ones. Second line displays the condensate densities $|\psi_1|^2$, $|\psi_2|^2$ and $|\psi_3|^2$. The last line shows the supercurrent moduli $|J_1|$, $|J_2|$ and $|J_3|$.
1. Composite soliton formation - Mechanism 1 :


This simulation starts with an initial compact distribution of vortices. While expanding, because of strong repulsive interactions, the system forms domains of two inequivalent ground states. Different ground states are separated by domain walls which tend to capture vortices. Contrary to a closed bare domain wall which shrinks because of its line tension, a closed domain wall decorated with vortices can be stabilize due to repulsive interactions between the vortices. A decorated domain wall touching the boundary, emits vortices and then moves out the numerical grid.
2. Composite soliton formation - Mechanism 2 :


This system has initially a closed domain wall, which shrinks because of its own line tension. In the process it decorates with vortices, stretching the domain wall until being emitted through boundary. In the centre, a small decorated closed domain wall has been formed by collision of vortices. This small domain wall reaches its equilibrium size, which is compromise between vortex repulsion and domain wall tension.