The general scheme for higher-order decompositions of zero-curvature equations associated with \(\widetilde {sl}(2)\) (Q1367103)

Within the framework of zero-curvature representation theory, the authors give a unified treatment on the decomposition of each equation in a hierarchy of zero-curvature equations associated with the loop algebra \(\widetilde{sl}(2)\) by means of higher-order constraints on a potential, and propose the general scheme and uniform formulae for the decompositions. 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.