  Recently it was demonstrated that magnon condensation in the trap exhibits
the phenomenon of self-localization. When the number of magnons in the textural
trap increases, they drastically modify the profile of the gap and highly
increase its size. The trap gradually transforms from the initial harmonic one
to the box with walls almost impenetrable for magnons. The resulting
texture-free "cavity" filled by the magnon condensate wave function becomes the
bosonic analog of the MIT bag, in which hadron is seen as a cavity surrounded
by the QCD vacuum, in which the free quarks are confined in the ground or
excited state. Here we consider the bosonic analog of the MIT bag with quarks
on the ground and excited levels.
