Rational solutions of the Kadomtsev–Petviashvili hierarchy and the dynamics of their poles. I. New form of a general rational solution

A new approach to the construction of the rational solutions to the hierarchy of the Kadomtsev–Petviashvili equation is presented. The generalization of the ‘‘superposition formula’’ is found to permit the construction of a new general solution from some partial ones. The features of the general polynomial factorization and the types of scattering in the many-body Calogero–Moser problem are investigated.