Hunter-Saxton方程：对称性和守恒密度的显著结构
The Hunter-Saxton equation: remarkable structures of symmetries and conserved densities
摘要：
在本文中，我们提出了非凡的代数和几何结构的Hunter-Saxton方程：无穷多个交换和非交换$x,t$ -独立的高阶对称性和守恒密度。使用递归关系，我们显式生成无限多个依赖于任意参数的高阶保守密度。我们发现三个Nijenhuis递归算子产生的哈密顿对，其中两个是新的。他们产生三个层次的交换局部对称。最后，我们给出了一个依赖于任意参数的局部递归算子。作为一个副产品，我们分类所有反对称运营商的一个明确的形式，是兼容的汉密尔顿运营商$D_x^{-1}$。
英文摘要：
In this paper, we present extraordinary algebraic and geometrical structures for the Hunter-Saxton equation: infinitely many commuting and non-commuting $x,t$-independent higher order symmetries and conserved densities. Using a recursive relation, we explicitly generate infinitely many higher order conserved densities dependent on arbitrary parameters. We find three Nijenhuis recursion operators resulting from Hamiltonian pairs, of which two are new. They generate three hierarchies of commuting local symmetries. Finally, we give a local recursion operator depending on an arbitrary parameter. As a by-product, we classify all anti-symmetric operators of a definite form that are compatible with the Hamiltonian operator $D_x^{-1}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
