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arXiv · 1011.5752

Constraints and Soliton Solutions for the KdV Hierarchy and AKNS Hierarchy

NianHua Li·YuQi Li
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Abstract

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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NianHua Li, YuQi Li. 2010-11-26. Constraints and Soliton Solutions for the KdV Hierarchy and AKNS Hierarchy. https://doi.org/10.1088/0253-6102%2F56%2F4%2F01

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