非对易torus上的新孤子解

New Soliton Solutions in Noncommutative Torus

利用在非对易可积torus(环)上的算子都有约化矩阵这一特点,孤子解的求解问题可以化为求满足代数方程Q(M)=0的有限维矩阵解问题．本文研究了当矩阵M不可对角化时的情形,分析这种情形,得到当势函数V(φ)具有三阶以上的极值点时,有限维矩阵方程V’(M)=0存在不可对角化的矩阵解．研究了这种解的一般形式,并通过kq表象,构造了非对易整环上以上述矩阵解为约化矩阵的新孤子解．根据这种构造方法,可以得到非对易orbifold上的新孤子解．

Besed on finite dimensional reduced matrices of operators on integral noncommutative torus, soliton solution problem can be converted into the finite matrix solution problem satisfying the algebraic equation Q（M）=0. In this paper, we mainly study the condition of reduced matrix for the operator which cannot be diagonalized. When the potential function V（φ） = 0 has an extremum point in three or more rank, there exist matrix solution that cannot be diagonalized for the finite dimensional matrix equation V’（M）=0. We study the general form of the solution and construct new soliton solution on noncommutative integral ring. In terms of the construction method, we obtain soliton solutions on noncommutative orbifold.