Some Stationary Solutions of Schrödinger Map Equation

Abstract

In this paper, we construct a type of plane wave solution of Landau-Lifshitz equation with the model | u | = 1. In addition, we discover the law which when the spin vector u is moving along one direction, the spin vector u approaches the south pole (0, 0, −1) from the north pole (0, 0, 1) with the model | x | from 0 tend to ∞. Landau-Lifshitz equations describe an evolution of spin field in continuous ferromagnetic. Therefore, it is very significant to study the problems about magnetization movement. Many people studied a lot of problems and constructed many solutions about the Landau-Lifshitz equation, but no one to study the linear plane wave solution. So, in this paper, we construct some stationary solutions of Schrodinger Map equation which contains a style of plane wave solutions.