Modified DKP hierarchy as modified BKP hierarchy

In this paper, we investigate some topics involving the modified D-type Kadomtsev-Petviashvili (DKP) hierarchy. Note that the modified DKP (mDKP) hierarchy is just the modified B-type Kadomtsev-Petviashvili (BKP) hierarchy in the bosonic forms. Based on this fact, we first proved the conjecture in You [Physica D 50, 429-462 (1991)], that is, the product of the two tau functions of the mDKP hierarchy is some tau function of the KP hierarchy. Then, we investigate the Darboux transformations of the DKP and mDKP hierarchy. Finally, the solutions of the constrained BKP hierarchy are given in the context of the fermionic representation of infinite Lie algebra d(infinity). Published under an exclusive license by AIP Publishing.

Automated summary

In this paper, we investigate several topics related to the modified D-type Kadomtsev-Petviashvili (DKP) hierarchy. We first prove a conjecture that the product of the two tau functions in the modified DKP hierarchy is a tau function in the KP hierarchy. Then, we study the Darboux transformations of the DKP and modified DKP hierarchies. Finally, we provide solutions for the constrained BKP hierarchy in the fermionic representation of the infinite Lie algebra d(infinity).