Spontaneous symmetry breaking in dual-core baby-Skyrmion systems

We introduce a system composed of two (2+1)-dimensional baby-Skyrmion models (BSMs) set on parallel planes and linearly coupled by tunneling of fields. This system can be realized in a dual-layer ferromagnetic medium. Unlike dual-core models previously studied in nonlinear optics and Bose-Einstein condensates, here the symmetry-breaking bifurcation (SBB) in solitons (baby Skyrmions) occurs with the increase of the intercore coupling (κ), rather than with its decrease, due to the fact that, even in the uncoupled system, neither core may be empty. Prior to the onset of the symmetry breaking between the two components of the solitons, they gradually separate in the opposite directions, due to the increase of κ, which is explained in an analytical form by means of an effective interaction potential. Such evolution scenarios are produced for originally symmetric states with topological charges in the two cores, B(1)=B(2)=1, 2, 3, 4. The evolution of mixed states, of the (B(1),B(2))=(1,2) and (2,4) types, with the variation of κ is studied too.