On Recursion Operator of the q-KP Hierarchy*Supported by the National Natural Science Foundation of China under Grant Nos. 11271210 and 11201451, and Anhui Province Natural Science Foundation under Grant No. 1608085MA04. (1st September 2016) - Tian 田, Ke-Lei 可雷; Zhu 朱, Xiao-Ming 晓鸣; He 贺, Jing-Song 劲松
Abstract: It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy. The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived.