Soliton and Domain Wall in the Self-Dual CP(1) Model

We perform the dimensional reduction of the nonrelativistic CP(1) model coupled to an Abelian Chern-Simons gauge field in the self-dual limit, and investigate the soliton and domain wall solutions of the emerging 1+1 dimensional self-dual spin system. This system is described by inhomogeneous Landau-Lifshitz system with an extra non-local term. The Hamiltonian is Bogomol'nyi bounded from below and has four adjusting parameters. The Bogomol'nyi equation is described in detail in analogy with the Newtonian equation of motion and its numerical solution is presented.