We consider integrability structures of the generalized Hunter–Saxton equation. We obtain the Lax representation with non-removable spectral parameter, find local recursion operators for symmetries and cosymmetries, generate an infinite-dimensional Lie algebra of higher symmetries, and prove existence of infinite number of cosymmetries of higher order. Further, we give examples of employing the higher order symmetries to constructing exact globally defined solutions for the generalized Hunter–Saxton equation.

中文翻译：

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广义Hunter-Saxton方程的可积性结构

我们考虑广义Hunter-Saxton方程的可积性结构。我们获得具有不可移动的光谱参数的Lax表示，找到对称性和对称性的局部递归算子，生成具有更高对称性的无限维李代数，并证明存在无限数量的更高阶对称性。此外，我们给出了使用高阶对称性为广义的Hunter-Saxton方程构造精确的全局定义解的示例。