  Based on the phenomenological Ginzburg-Landau approach, we investigate phase
solitonic states in a class of three-component superconductors for mesoscopic
doubly-connected geometry (thin-walled cylinder) in external magnetic fields.
Analysis of the Gibbs free energy of the system shows that solitonic states in
a three-component superconductor are thermodynamically metastable and separated
from the ground state by a sizable energy. Our results demonstrate that despite
of the presence of the zoo of phase solitons states earlier proposed method
[Phys. Rev. B 96, 144513 (2017)] for the detection of BTRS in multiband
superconductors remains valid and useful.
