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We consider a scalar field model with a self-interaction potential thatpossesses a discrete vacuum manifold. We point out that this model allows forboth topological as well as non-topological solitons. In (1+1) dimensions bothtype of solutions have finite energy, while in (3+1) dimensions, thetopological solitons have finite energy per unit area only and correspond todomain walls. Non-topological solitons with finite energy do exist in (3+1)dimensions due to a non-trivial phase of the scalar field and an associatedU(1) symmetry of the model, though. We construct these so-called Q-ballsolutions numerically, point out the differences to previous studies withdifferent scalar field potentials and also discuss the influence of a minimalcoupling to both gravity as well as a U(1) gauge field. In this latter case,the conserved Noether charge Q can be interpreted as the electric charge of thesolution.

From topological to non-topological solitons: kinks, domain walls and Q-balls in a scalar field model with non-trivial vacuum manifold