Hunter-Saxton族拟周期解的另一种方法
An alternative approach to the quasi-Periodic solutions of the Hunter-Saxton hierarchy
摘要：
本文给出了包含Hunter-Saxton（HS）方程的一个新的交换族的所有方程的代数几何型整体解.我们的主要工具包括零曲率方法导出HS族，广义雅可比簇，广义黎曼θ函数，Weyl $m$ -函数$m_\pm(x,t,z)$，和通过求解Sturm-Liouville方程$L(ψ_1)=-ψ_1^{\prime\prime}=zyψ_1$的反问题得到的极点运动。基于这些工具和非自治微分系统理论，拓扑动力学和遍历理论，得到了整个HS族的代数几何解。
英文摘要：
This paper is dedicated to provide the global solutions of algebro-geometric type for all the equations of a new commuting hierarchy containing the Hunter-Saxton (HS) equation. Our main tools include the zero curvature method to derive the HS hierarchy, the generalized Jacobian variety, the generalized Riemann theta function, the Weyl $m$-fucntions $m_\pm(x,t,z)$, and the pole motion obtained by solving an inverse problem for the Sturm-Liouville equation $L(ψ_1)=-ψ_1^{\prime\prime}=zyψ_1$. Based on these tools and the theory of nonautonomous differential systems, topological dynamics and ergodic theory, the algebro-geometric solutions are obtained for the entire HS hierarchy.
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