Symmetries and bilinear equations for the modified BKP hierarchy.

The modified Kadomtsev-Petviashvili hierarchy of B type (mBKP hierarchy) and its constrained cases are investigated from the aspect of the Lax formulation. Starting from the Lax equation of the mBKP hierarchy, we firstly derive the bilinear equations and show the existence of the tau functions. Then the additional symmetries are constructed, and the corresponding generator is showed to be the squared eigenfunction symmetry. After that, the actions of the additional symmetries on the tau functions are given. At last, the Lax formulation of the constrained mBKP hierarchy is investigated and the corresponding bilinear equations are also discussed. [ABSTRACT FROM AUTHOR]