标题： 显式流方程和ncKP层次的递归算子 显示英文标题

标题： Explicit Flow Equations and Recursion Operator of the ncKP hierarchy

摘要： 非交换Kadomtsev-Petviashvili(ncKP)层次的流方程的显式表达式被推导出来。与KP层次的流方程相比，我们的结果表明ncKP层次的流方程中的附加项确实由动力坐标\{$u_i$\}的对易子组成。给出了在$n$约化下的流方程的递归算子。进一步地，在2约化下，我们计算了非交换Korteweg-de Vries(ncKdV)层次的一个非局部递归算子$\Phi(2)$，该算子生成一组局部的高阶流。因此，我们解决了P.J. Olver和V.V. Sokolov(Commun.Math.Phys. 193 (1998), 245-268)提出的一个开放问题。 显示英文摘要

摘要： The explicit expression of the flow equations of the noncommutative Kadomtsev-Petviashvili(ncKP) hierarchy is derived. Compared with the flow equations of the KP hierarchy, our result shows that the additional terms in the flow equations of the ncKP hierarchy indeed consist of commutators of dynamical coordinates \{$u_i$\}. The recursion operator for the flow equations under $n$-reduction is presented. Further, under 2-reduction, we calculate a nonlocal recursion operator $\Phi(2)$ of the noncommutative Korteweg-de Vries(ncKdV) hierarchy, which generates a hierarchy of local, higher-order flows. Thus we solve the open problem proposed by P.J. Olver and V.V. Sokolov(Commun.Math.Phys. 193 (1998), 245-268).