Summary
Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. A binary non-linearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of commutative, finite-dimensional integrable Hamiltonian systems in the Liouville sense, which also provides us with new examples of finite-dimensional integrable Hamiltonian systems. A sort of involutive solutions to the Kaup-Newell hierarchy are exhibited through the obtained finite-dimensional integrable systems and the general involutive system engendered by binary non-linearization is reduced to a specific involutive system generated by mono-non-linearization.
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Ma, W.X., Ding, Q., Zhang, W.G. et al. Binary non-linearization of Lax pairs of Kaup-Newell soliton hierarchy. Nuov Cim B 111, 1135–1149 (1996). https://doi.org/10.1007/BF02743224
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DOI: https://doi.org/10.1007/BF02743224