论文标题
Miura转换的几何方面
Geometric aspects of Miura transformations
论文作者
论文摘要
Miura转化在可集成系统的研究中起着至关重要的作用。 Miura转换有各种扩展，这些扩展已用于关联不同种类的集成方程并分类Bi-Hamiltonian结构。在本文中，我们主要关注Miura转化的几何方面。从MKDV型层次结构到KDV型层次结构的广义miura转换均在代数和几何设置下构建。结果表明，MIURA变换不仅关联了不同几何形状中的可集成曲线流，而且还引起了不同移动帧之间的过渡。还研究了其他几何配方。
The Miura transformation plays a crucial role in the study of integrable systems. There have been various extensions of the Miura transformation, which have been used to relate different kinds of integrable equations and to classify the bi-Hamiltonian structures. In this paper, we are mainly concerned with the geometric aspects of the Miura transformation. The generalized Miura transformations from the mKdV-type hierarchies to the KdV-type hierarchies are constructed under both algebraic and geometric settings. It is shown that the Miura transformations not only relate integrable curve flows in different geometries but also induce the transition between different moving frames. Other geometric formulations are also investigated.
