论文标题
仿射Toda层次结构的广义反弹转换
Generalized Backlund transformations for Affine Toda Hierarchies
论文作者
论文摘要
$ a_n $ affine toda层次结构的广义反弹转换的构建是根据对零曲率表示的量规变换而提出的。这种结构基于基础仿射代数的分级结构，该结构诱导了广义反弹转换的分类。此外，$ su（3）$和$ su（4）$的明确示例导致发现各种反向悬浮转换的有趣构图属性。仪表 - 贝克伦转换方法的通用特征扩展到层次结构的所有方程式。这种有趣的属性提供了一个系统的框架，可以构建向更高流程方程的backlund转换。列出了$ SL（3）$层次结构的最简单较高流量的明确示例。
The construction of generalized Backlund transformation for the $A_n$ Affine Toda hierarchy is proposed in terms of gauge transformation acting on the zero curvature representation. Such construction is based upon the graded structure of the underlying affine algebra which induces a classification of generalized Backlund transformations. Moreover, explicit examples for $su(3)$ and $su(4)$ lead to uncover interesting composition properties of various types of Backlund transformations. The universality character of the gauge-Backlund transformation method is extended to all equations of the hierarchy. Such interesting property provides a systematic framework to construct Backlund transformations to higher flow equations. Explicit example for the simplest higher flow of the $sl(3)$ hierarchy is presented.
