Sato–Bäcklund transformations and string equations of the mKP hierarchy.

Additional symmetry is an important kind of symmetries depending explicitly on the time and space variables, which can be expressed through Sato–Bäcklund transformations. In this paper, we construct Sato–Bäcklund transformations of the modified KP hierarchy and its constrained cases. Then the string equations of the p -reduced modified KP hierarchy are established by requiring the system independent on some additional symmetry flows, which are expressed by the Lax operator L and the Orlov–Shulman's operator M. At last, we obtain the negative Virasoro constraint on the two tau functions of the 2-reduced modified KP hierarchy satisfying the string equations. [ABSTRACT FROM AUTHOR]