关于KP方程主对称的换位运算公式的一点注记

KP方程(1) 具有无限的对称和守恒常数,它们分别构成Lie代数,这些是熟知的事实,在换位运算(2) 之下,KP方程的主对称也构成一个Lie代数,其中。“′”表示加脱导数:

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．

A NOTE WITH REGARD TO A FORMULA OF COMMUTATION RELATIONS OF THE MASTER SYMMETRIES FOR KP EQUATIONS

there are infinite symmetries and infinite conserved constants, and they form Lie algebras respectively. Under the commutation relation :

LAX PAIR OF A COUPLED NONLINEAR WAVE EQUATIONS

Symmetries and conservations of the coupled nonlinear equations were discussed. Using the prolongation methods, we have found that, for Eqs. (1) and (2), there exists a Lax pair:

Double Darboux Transformation for AKNS Hierarchy

In this paper we construct a double Darboux Transformation for AKNS hierarchy and give its decomposition theorem.A remarkable characteristic of the double Darboux Transforma- tion - incommutativity is proved.