We develop a formalism of multicomponent BKP hierarchies using elementary geometry of spinors. The multicomponent KP and the modified KP hierarchy (hence all their reductions like KdV, NLS, AKNS or DS) are reductions of the multicomponent BKP.

where τ0 = 1. The τ -functions τn are given by the pfaffians of certain skew-symmetric matrix. We identify one-soliton solution as an element of the Weyl group of D-type, and discuss a general structure of the interaction patterns among the solitons. Soliton solutions are characterized by 4N × 4N skew-symmetric constant matrix which we call the B-matrices. We then find that one can have M -soli...