The general scheme for higher-order decompositions of zero-curvature equations associated with 337-1337-1337-1(2)

Within the framework of zero-curvature representation theory, the decompositions of each equation in a hierarchy of zero-curvature equations associated with loop algebra by means of higher-order constraints on potential are given a unified treatment, and the general scheme and uniform formulas for the decompositions are proposed. This provides a method of separation of variables to solve a hierarchy of (1+1)-dimensional integrable systems. To illustrate the general scheme, new higher-order decompositions of two hierarchies of zero-curvature equations are presented.This project is supported by the National Basic Research Project Nonlinear Science.