Some Research On The Schr(?)dinger Map Equation

The Schr?dinger map equation describes the ferromagnets with an easy-plan anisotropy,so it plays an important role in ferromagnetic theory.On the basis of the Landau-Lifshitz equation describing the planar ferromagnets as the background,we can obtain the static and spherically symmetric solutions of the planar Schr?dinger map equation.At the same time,with construct similar solutions and perturbation method,we study traveling wave solutions of the Schr?dinger map equations.In addition,we establish the central difference scheme of the Schr?dinger map equation for the initial-boundary value problems and analyzes the truncation error of the difference scheme under its special circumstance.Finally,we simulate the difference and compare with the exact solutions by Matlab software.