Q-lumps on a Domain Wall with a Spin-Orbit Interaction

The nonlinear O(3) sigma-model in (2+1) dimensions with an additional potential term admits solutions called Q-lumps, having both topological and Noether charges. We consider in 3+1-dimensional spacetime the theory with Q-lumps on a domain wall in the presence of spin-orbit interaction in the bulk and find interaction effects for a two-particle solution through perturbation theory and adiabatic approximation.