  Quasi-symmetric functions show up in an approach to solve the
Kadomtsev-Petviashvili (KP) hierarchy. This moreover features a new
nonassociative product of quasi-symmetric functions that satisfies simple
relations with the ordinary product and the outer coproduct. In particular,
supplied with this new product and the outer coproduct, the algebra of
quasi-symmetric functions becomes an infinitesimal bialgebra. Using these
results we derive a sequence of identities in the algebra of quasi-symmetric
functions that are in formal correspondence with the equations of the KP
hierarchy.
