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We study axially symmetrical 3D skyrmionic particles (torons, hopfions) in athin homeotropic cell filled with a cholesteric liquid crystal. In this case,the contribution of the chirality term on far distances becomes small and a 3Dskyrmion can be described as a very specific particle in nematic with multipolemoments of different chiralities. We show that small skyrmions asymptoticallycan be presented as a particle with six multipole moments. Thus, we find theexact analytical solution for the far field director configuration around the3D skyrmion and the exact analytical expression for the elastic interactionpotential between 3D skyrmions in a homeotropic cell with thickness $L$. Thecomparison with the experiment allows us to recover approximately multipolecoefficients of one small 3D skyrmion. We also describe the expansion of theskyrmion bag analytically depending on the number $N$ of anti-skyrmions in itand obtain an agreement with the experiment.  Along the way, we determined the director field around a chiral axiallysymmetric colloidal particle in the unlimited nematic liquid crystal and in theconfined homeotropic cell, taking into account higher order elastic terms withorders $l=1\div 6$. We also have found the elastic interaction potentialbetween such particles.

Theory of elastic interaction between axially symmetric 3D skyrmions in confined chiral nematic liquid crystals and in skyrmion bags