论文标题
广义猎人的可集成性结构 - -Saxton方程
Integrability structures of the generalized Hunter--Saxton equation
论文作者
论文摘要
我们考虑了广义猎人的可集成性结构 - -Saxton方程。特别是，我们获得了具有不可移动光谱参数的LAX表示，找到用于对称性和宇宙对称性的局部递归算子，产生一个较高对称性的无限维级代数，并证明存在无限量的cosymorties cosymorties。此外，我们举例说明使用高阶对称性来为广义猎人构建精确的全球定义解决方案 - 萨克斯顿方程。
We consider integrability structures of the generalized Hunter--Saxton equation. In particular, we obtain the Lax representation with nonremovable 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 an example of employing the higher order symmetry to constructing exact globally defined solutions for the generalized Hunter--Saxton equation.
