It is well-known that the finite-gap solutions of the KdV equation can be
generated by its recursion operator.We generalize the result to a special form
of Lax pair, from which a method to constrain the integrable system to a
lower-dimensional or fewer variable integrable system is proposed. A direct
result is that the n-soliton solutions of the KdV hierarchy can be completely
depicted by a series of ordinary differential equations (ODEs), which may be
gotten by a simple but unfamiliar Lax pair. Furthermore the AKNS hierarchy is
constrained to a series of univariate integrable hierarchies. The key is a
special form of Lax pair for the AKNS hierarchy. It is proved that under the
constraints all equations of the AKNS hierarchy are linearizable.Comment: 12 pages, 0 figur
