VECTOR NONLINEAR SCHRODINGER HIERARCHIES AS APPROXIMATE KADOMTSEV-PETVIASHVILI HIERARCHIES

The Kadomtsev-Petviashvili (KP) hierarchy, a collection of compatible nonlinear equations, each in 2 + 1 independent variables, can be consi stently constrained in many different ways to yield hierarchies of equ ations in 1 + 1 independent variables. In particular, the N-component vector nonlinear Schrodinger (VNLS) hierarchies are contained within t he KP hierarchy in this way. These hierarchies approximate the KP hier archy in the limit of large N, and this permits the equations of the K P hierarchy to be approximated by nonlinear equations in 1 + 1 dimensi ons.