摘要
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u2k+1能被偶数阶动力学变量u2k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.
In this paper, under the constraints of the BKP （CKP） hierarchy, a crucial observation is that the odd dynamical variable U2k＋l can be explicitly expressed by the even dynamical variable u2k 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 tl flows by the above recursion operators, which are consistent with the corresponding flows generated by the flow equations under 3-reduction.
出处
《中国科学：数学》
CSCD
北大核心
2013年第5期499-514,共16页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:10971109和11271210)
宁波大学科研基金(批准号:xk1062和XYL11012)资助项目
