Darboux transformations of noncommutative BKP and CKP hierarchies

摘要

In this paper, we construct Darboux transformations of the noncommutative BKP (ncBKP) hierarchy and the noncommutative CKP (ncCKP) hierarchy. Prom these Darboux transformations, the explicit differences between the BKP (CKP) hierarchy and the noncommutative BKP (ncCKP) hierarchy can be seen clearly in this paper. These studies might be useful in the M theory and string theory in future.