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Soliton and Domain Wall in the Self-Dual Ferromagnet

We perform the dimensional reduction of a uniaxial planar ferromagnet system 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 system. This self-dual ferromagnet is the usual inhomogeneous Landau-Lifshitz system with an extra non-local term supplementing the anisotropic potential energy. 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. PACS codes: 11.10.Lm, 11.27.+d