论文标题
具有非平坦统一和可整合层次结构的广义弗罗贝尼乌斯歧管
Generalized Frobenius Manifolds with Non-flat Unity and Integrable Hierarchies
论文作者
论文摘要
对于任何具有非灯泡统一的普通Frobenius歧管，我们构建了一个Bihamiltonian的流体动力类型的可集成层次结构，这是Frobenius歧管的主要层次结构的类似物。我们表明，我们称之为主要层次结构的这种可集成的层次结构具有Virasoro对称性和TAU结构，并且可以将Virasoro对称性提升为可集成层次结构的Tau封面的对称性。我们从virasoro对称对tau函数的作用的线性化的条件中得出了循环方程，并构建了具有非flat unity的半密布弗罗贝尼乌斯歧管的主层次层次结构的拓扑变形。我们还提供了两个具有非平坦统一的普遍的Frobenius歧管的例子，并表明它们与众所周知的可集成层次结构密切相关：Volterra层次结构，Q- Q-emeded KDV层次结构和Ablowitz-Ladik层次结构。
For any generalized Frobenius manifold with non-flat unity, we construct a bihamiltonian integrable hierarchy of hydrodynamic type which is an analogue of the Principal Hierarchy of a Frobenius manifold. We show that such an integrable hierarchy, which we also call the Principal Hierarchy, possesses Virasoro symmetries and a tau structure, and the Virasoro symmetries can be lifted to symmetries of the tau-cover of the integrable hierarchy. We derive the loop equation from the condition of linearization of actions of the Virasoro symmetries on the tau function, and construct the topological deformation of the Principal Hierarchy of a semisimple generalized Frobenius manifold with non-flat unity. We also give two examples of generalized Frobenius manifolds with non-flat unity and show that they are closely related to the well-known integrable hierarchies: the Volterra hierarchy, the q-deformed KdV hierarchy and the Ablowitz-Ladik hierarchy.
