Some New Solutions of the Landau-Lifshitz Equation in Cylindrical Symmetric System

This paper is devoted to obtaining various explicit dynamic solutions of the Landau-Lifshitz equation in 2-dimensional cylindrical symmetric system. By suitably establishing explicit transformation, we here construct explicit dynamic solutions depending on the angle θ and time t for Landau-Lifshitz equation with anisotropy field or external magnetic field. Besides, we introduce certain indeterminate solution form of the Landau-Lifshitz equation by solving the indeterminate coefficients to derive explicit magnetic vortex or traveling wave solution. In this paper, we provide some specific examples and attain their some explicit dynamic solutions.