Abstract The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons (magnetic vortices) in ferromagnets and anti-ferromagnets.It is achieved through the conservation laws for the topological vorticity and the weak convergence methods.
LIN Fang-hua, SHATAH Jalal. Soliton dynamics in planar ferromagnets and anti-ferromagnets. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2003, 4(5): 503-510.