Darboux transformations of the modified BKP hierarchy by fermionic approach

Abstract

The modified BKP (mBKP) hierarchy is an important integrable hierarchy related with BKP hierarchy. Darboux transformation is a powerful method to obtain various solutions of integrable systems. But for mBKP hierarchy, it is usually very difficult to construct the corresponding Darboux transformations, since it has a more complicated constraint on the Lax operator, compared with the BKP hierarchy. In this paper, we use the fermionic approach to obtain the explicit Darboux transformation operators of the mBKP hierarchy starting from the changes in tau functions. Also we investigate the relations among these new Darboux transformation operators. It is usually very difficult to convert the changes in tau functions to the ones in the Lax operator, while here we provide one successful example.