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Within the framework of zero-curvature representation theory, the decompositions of each equation in a hierarchy of zero-curvature equations associated with loop algebra $$\widetilde{sl}(2)$$ 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.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 16, 2005
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