薛定谔映射问题的k等变解的性质

The Nature for k-Equivariant Solutions to the Schrodinger Map Problem

摘要: 薛定谔映射问题中的等变解的同伦指数k与解本身是有一定的关系的，可以通过定义的拓扑度来表达。举了一个例子验证了一下，没有证明。但证明了方程保证了解的狄里克雷能量是保持不变的，并计算出了随着初值变化，解的能量的最小值。

Abstract: K-equivariant solutions have a relationship with its homotopy index k in the Schrodinger map problem. We can explain it by topological degree. We give an example to verify it without certification. Then we proved that the equation keeps the Dirichlet energy constant. At last we calculate its minimum value.