New Subhierarchies of the KP Hierarchy in the Sato Theory. II. Truncation of the KP Hierarchy

Abstract

New subhierarchies of the KP hierarchy in the Sato theory, named the m-truncated KP hierarchies (m=1, 2, …), are presented. The simplest one of the case m=1 is the Burgers-Hopf hierarchy, which is transformed into a system of linear equations, while other cases are into systems of linear and nonlinear equations. On account of the linear equations, the multiplicity of soliton solutions is limited up to m for the m-truncated KP hierarchy. It is also shown that the solution space of the m-truncated KP hierarchy is a submanifold “GM(m, ∞)” of the universal Grassmann manifold UGM, which is the solution space of the full KP hierarchy.