摘要
Q-形变的modified Kadomtsev-Petviashvili(q-mKP)系列是经典mKP系列的量子化推广,其流方程包括无穷多个微分方程簇,流方程的等价形式是一个广为关注的问题.类似于对mKP系列的研究,尝试沿着Sato理论框架,基于其Lax算子、Lax方程,给出该可积系列流方程的等价形式,这些结果显示出q-mKP系列与mKP系列的不同,并不是mKP系列的简单,是进一步探讨其递归算子、代数约束等可积性质的基础.
The q-deformed modified Kadomtsev Petviashvili （q-mKP） hierarchy is the quantum deformation of classical mKP hierarchy. The flow equations of q mKP hierarchy contain infinite differential equations. The equivalent formulas for the flow equations of q mKP hierarchy attract many attentions. It is the aim of the present article to give the equivalent formulas for flow equations of q mKP hierarchy via I.ax operator and I.ax equation in Sato theory. These results show that q mKP hierarchy is not a trivial formalism generalization of the mKP hierarchy. There exist at least several topics needed to be discussed in order to research the integrability property of q mKP hierarchy based on the results in the paper. For instance, the recursion operator for the flow equations of q mKP hierarchy; the algebraic constraint for q mKP hierarchy.
作者
张秋晨
ZHANG Qiu chen(School of Mathematics, Hefei University of Technology, Hefei 230009, Chin)
出处
《大学数学》
2018年第2期26-30,共5页
College Mathematics
基金
国家自然科学基金(11671371)
安徽省自然科学基金(1608085MA04)
