On the constrained B-type Kadomtsev–Petviashvili hierarchy: Hirota bilinear equations and Virasoro symmetry

Abstract

We derive the bilinear equations of the constrained BKP hierarchy from the calculus of pseudodifferential operators. The full hierarchy equations can be expressed in Hirota's bilinear form characterized by the functions ρ, σ, and τ. Besides, we also give a modification of the original Orlov–Schulman additional symmetry to preserve the constrained form of the Lax operator for this hierarchy. The vector fields associated with the modified additional symmetry turn out to satisfy a truncated centerless Virasoro algebra.