Rational solutions of the KP hierarchy and the dynamics of their poles. II. Construction of the degenerate polynomial solutions

A general approach to constructing the polynomial solutions satisfying various reductions of the Kadomtsev–Petviashvili (KP) hierarchy is described. Within this approach, the reductions of the KP hierarchy are equivalent to certain differential equations imposed on the τ-function of the hierarchy. In particular, the l-reduction and the k-constraint as well as their generalized counterparts are considered. A general construction of the rational …