Skyrmion-like excitations in dynamical lattices

We construct discrete analogs of Skyrmions in nonlinear dynamical lattices. The Skyrmion is built as a vortex soliton of a complex field, coupled to a dark radial soliton of a real field. Adjusting the Skyrmion ansatz to the lattice setting allows us to construct a "baby-Skyrmion" in two dimensions (2D) and extend it into the 3D case (1D counterparts of the Skyrmions are also found). Stability limits for these patterns are obtained analytically and verified numerically. The dynamics of unstable discrete Skyrmions is explored, and their stabilization by external potentials is discussed.