Some Stationary Solutions of Schrödinger Map Equation
Yanting Zhou
Institute of Mathematics, Yunnan Normal University, Kunming, 650500, China.
Hui Yang
Institute of Mathematics, Yunnan Normal University, Kunming, 650500, China.
Ganshan Yang *
Institute of Mathematics, Yunnan Normal University, Kunming, 650500, China and Department of Mathematics, Yunnan Minzu University, Kunming, 650504, China.
*Author to whom correspondence should be addressed.
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.
Keywords: Landau-Lifshitz equations, Schrödinger Map equation, stationary solution, dynamical solution.