BKP 与CKP 可积系列的递归算子

借助于新引进的算子B, 本文给出了BKP 与CKP 可积系列约束条件在其Lax 算子L中的动力学变量上的具体体现, 即奇数阶动力学变量u_2k+1 能被偶数阶动力学变量u_2k 显式表达. 同时本文给出了BKP 与CKP 可积系列的流方程以及(2n + 1)- 约化下递归算子的统一公式, 揭示了BKP 可积系列和CKP 可积系列的重要区别. 作为例子, 本文给出了BKP 与CKP 可积系列在3- 约化下的递归算子的显式表示, 并验证了u₂ 的t₁ 流通过递归算子的确可以产生u₂ 的t₇ 流, 该流方程与3- 约化下产生的对应流方程是一致的.

The recursion operators of the BKP hierarchy and the CKP hierarchy

In this paper, under the constraints of the BKP (CKP) hierarchy, a crucial observation is that the odd dynamical variable u_2k+1 can be explicitly expressed by the even dynamical variable u_2k in the Lax operator L through a new operator B. Using operator B, the essential differences between the BKP hierarchy and the CKP hierarchy are given by the flow equations and the recursion operators under the (2n + 1)-reduction. The formal formulas of the recursion operators for the BKP and CKP hierarchy under (2n + 1)-reduction are given. To illustrate this method, the two recursion operators are constructed explicitly for the 3-reduction of the BKP and CKP hierarchies. The t₇ flows of u₂ are generated from t₁ flows by the above recursion operators, which are consistent with the corresponding flows generated by the flow equations under 3-reduction.