KP系统Lax算子及主对称的换位公式

本文讨论的是ＫＰ系统Ｌａｘ算子及主对称的换位公式．通过拓广速降函数空间及对 ＫＰ方程 Ｌａｘ算子的讨论，找到了 Ｌａｘ算子的表示向量；并通过对 Ｌａｘ算子、 Ｌａｘ流、 Ｌａｘ算子表示向量之间联系的讨论，得出了计算 Ｌａｘ算子李括号的表示向量的方法，从而解决了 ＫＰ方程主对称的换位公式问题．最后本文还利用伴随算子给出了从ＫＰ方程任一主对称得到其一个对称的公式．

Commutation Formulas of Two Lax Operator and Two Master Symmetries for KP Hierarchy

This paper mainly concerns about the commutation formulas of Lax operators and masters symmetries for KP hierarchy. At first the quickly decaying function space is extended and the condition for operator to be Lax operator is discussed. On the basis of above work, the representation vector of Lax operator is found. Then, by studying the relationship among the Lax operator, Lax flow and the representa- tion vector of Lax operator, a method to calculate the representation vector of the Lie bracket of two Lax operators as well as a method to calculate the commutation of two master symmetries are obtained. At the end of this paper,a formula that can be used to obtain a symmetry from an arbitrary master symmetry is also given.