Additional symmetries and string equations of the noncommutative B and C type KP hierarchies. Issue 1 (2nd January 2017) - Liu, Qiufang; Li, Chuanzhong
Abstract : In this paper, we construct the noncommutative B and C type KP hierarchies using pseudo-differential operators and reducing conditions. Further a series of additional flows of the noncommutative B and C type KP hierarchies will be defined and the additional symmetries constitute the B and C type infinite dimensional Lie algebra W 1+∞ . In addition, the generating function of the additional symmetries can also be proved to have a nice form in terms of wave functions. Further, the string equations of the noncommutative B and C type KP hierarchies are derived.