Trigonal curves and algebro-geometric solutions to soliton hierarchies II
Trigonal curves and algebro-geometric solutions to soliton hierarchies II
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DOI：
10.1098/rspa.2017.0233
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发表时间：
2017
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通讯作者：
W. Ma
中科院分区：
文献类型：
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作者：
W. Ma
这是对孤子层次代代几何解的黎曼 theta 函数表示研究的延续。在这一部分中，我们在确定 Baker-Akhiezer 函数的黎曼 theta 函数表示后，理顺与 Lax 对相关的 Abel-Jacobi 坐标下的孤子层次中的所有流，并通过观察 Baker-Akhiezer 函数的渐近行为，根据黎曼 theta 函数生成孤子层次的代代几何解。我们强调，我们以这样一种方式分析四分量 AKNS 孤子层次，从而得出适用于构造任意孤子层次的代数几何解的三角曲线的一般理论。
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.