  The existence of thresholdless vortex solitons trapped at the core of
disclination lattices that realize higher-order topological insulators is
reported. The study demonstrates the interplay between nonlinearity and
higher-order topology in these systems, as the vortex state in the disclination
lattice bifurcates from its linear topological counterpart, while the position
of its propagation constant within the bandgap and localization can be
controlled by its power. It is shown that vortex solitons are characterized by
strong field confinement at the disclination core due to their topological
nature, leading to enhanced stability. Simultaneously, the global discrete
rotational symmetry of the disclination lattice imposes restrictions on the
maximal possible topological charge of such vortex solitons. The results
illustrate the strong stabilizing action that topologically nontrivial
structures may exert on excited soliton states, opening new prospects for
soliton-related applications.
