论文标题
Stäckel固定KDV系统的表示
Stäckel representations of stationary KdV systems
论文作者
论文摘要
在本文中，我们研究了固定KDV系统的Stäckel表示。使用宽松的形式主义，我们证明这些系统具有两种不同的表示，作为本丹蒂类型的可分离stäckel系统，与固定歧管的不同叶子有关。我们通过在固定KDV系统的喷射坐标和相应的Benenti Systems的分离变量之间构建明确的变换来做到这一点，以进行任意数量的自由度。此外，在固定歧管上，我们介绍了固定KDV系统的两种表示形式的明确形式，这也产生了他们的双 - 汉密尔顿公式。
In this article we study Stäckel representations of stationary KdV systems. Using Lax formalism we prove that these systems have two different representations as separable Stäckel systems of Benenti type, related with different foliations of the stationary manifold. We do it by constructing an explicit transformation between the jet coordinates of stationary KdV systems and separation variables of the corresponding Benenti systems for arbitrary number of degrees of freedom. Moreover, on the stationary manifold, we present the explicit form of Miura map between both representations of stationary KdV systems, which also yields their bi-Hamiltonian formulation.
