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Trigonal curves and algebro-geometric solutions to soliton hierarchies II

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Ma, Wen-Xiu

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Royal Society

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This is a continuation of a study on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, we straighten out all flows in soliton hierarchies under the Abel-Jacobi coordinates associated with Lax pairs, upon determining the Riemann theta function representations of the Baker-Akhiezer functions, and generate algebro-geometric solutions to soliton hierarchies in terms of the Riemann theta functions, through observing asymptotic behaviours of the Baker-Akhiezer functions. We emphasize that we analyse the four-component AKNS soliton hierarchy in such a way that it leads to a general theory of trigonal curves applicable to construction of algebro-geometric solutions of an arbitrary soliton hierarchy.

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Ma, W. 2017. Trigonal curves and algebro-geometric solutions to soliton hierarchies II. Proceedings of the Royal Society A-mathematical Physical and Engineering Sciences, 473:1-20. [https://doi.org/10.1098/rspa.2017.0233]

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