论文标题
一类延长的高维非智能KDV层次结构和对称性
A class of extended high-dimensional nonisospectral KdV hierarchies and symmetry
论文作者
论文摘要
我们构建了一类新的N维谎言代数，并将其应用于可集成的系统。在本文中，我们通过引入非镜头光谱问题获得了非镜头KDV可集成的层次结构。然后，通过相应的高维环代数来推导耦合的非元素KDV层次结构。因此，研究了k对称，τ对称性及其耦合非镜面KDV层次结构的代数。两种结果层次结构的双 - 汉密尔顿结构都是通过使用痕量身份得出的。最后，我们得出了与n维环代数相关的多组分非元件KDV层次结构，该代数将耦合结果推广到任意数量的组件。
We construct a new class of N-dimensional Lie algebras and apply them to integrable systems. In this paper, we obtain a nonisospectral KdV integrable hierarchy by introducing a nonisospectral spectral problem. Then, a coupled nonisospectral KdV hierarchy is deduced by means of the corresponding higher-dimensional loop algebra. It follows that the K symmetries, τ symmetries and their Lie algebra of the coupled nonisospectral KdV hierarchy are investigated. The bi-Hamiltonian structures of the both resulting hierarchies are derived by using the trace identity. Finally, we derive a multi-component nonisospectral KdV hierarchy related to the N-dimensional loop algebra, which generalizes the coupled results to an arbitrary number of components.
