Constraints and Soliton Solutions for the KdV Hierarchy and AKNS Hierarchy

Details Constraints and Soliton Solutions for the KdV Hierarchy and AKNS Hierarchy Constraints and Soliton Solutions for the KdV Hierarchy and AKNS Hierarchy

2010-11-26

arxiv.org/abs/1011.5752v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, 0 figure

Scientific paper

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.

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