Algebro-Geometric Solutions of the Sine-Gordon Hierarchy
Algebro-Geometric Solutions of the Sine-Gordon Hierarchy
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DOI：
10.1007/s44198-022-00074-5
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发表时间：
2022-07
影响因子：
0.7
通讯作者：
Xue Geng;L. Guan
中科院分区：
文献类型：
--
作者：
Xue Geng;L. Guan
基于两组Lenard递归序列和与一个矩阵谱问题相关的零曲率方程，我们得到了由所有正流和负流组成的整个Sine-Gordon族。利用超椭圆曲线理论，引入Abel-Jacobi坐标，对相应的正、负流进行线性化。利用亚纯函数的渐近性质，构造了整个Sine-Gordon族的代数几何解。
On the basis of two sets of Lenard recursion sequences and zero-curvature equation associated with a matrix spectral problem, we derive the entire sine-Gordon hierarchy, which is composed of all the positive and negative flows. Using the theory of hyperelliptic curves, the Abel-Jacobi coordinates are introduced, from which the corresponding positive and negative flows are linearized. The algebro-geometric solutions of the entire sine-Gordon hierarchy are constructed by using the asymptotic properties of the meromorphic function.