Differential polynomial expressions related to the Kadomtsev–Petviashvili and Korteweg–de Vries hierarchies

Abstract

An integrable nonlinear partial differential equation typically extends to a hierarchy of integrable equations. There exist several recursive schemes for obtaining these hierarchies. Recently, explicit expressions for the KdV hierarchy have been found. We derive explicit expressions for the hierarchy associated with the KP equation. The main tools are Sato’s theory, Hirota’s formalism, and Bell’s polynomials.