超对称可积系统的对称性及局域激发

由于超对称可积模型在非微扰二维超引力，矩阵模型的超扩展和拓扑场理论中潜在的物理应用，超对称可积系统的研究引起了人们的浓厚兴趣。本项目拟对超对称可积系统展开以下研究：① 应用形变的方法，通过1+1 维超对称可积模型来构建2+1维超对称可积模型；② 将形式级数对称理论等方法推广到超对称的形式，得到高维超对称可积模型的无穷多对称及其Kac-Moody-Virasoro 型的代数结构；③ 利用Painleve分析对超对称可积模型进行完全可积性的测试；④ 寻找求解的新途径，探究超对称可积系统的局域激发及其相互作用。本项目的研究，将有助于揭示超对称可积系统的对称结构和基本性质，为超对称可积模型可能的物理应用提供理论参考。

Supersymmetric integrable systems have attracted an increasing amount of interest, mainly due to their potential physical applications in non-perturbative 2D supergravity, supertensions of matrix models and topological field theories. This project is devoted to the following investigations for some supersymmetric integrable systems: .①.Applying a method of deformation, we try to construct some supersymmetric integrable models in 2+1 dimensions starting from 1+1-dimensional supersymmetric integrable models;.②.By extending some approaches such as the Formal Series Symmetry Theory in term of supersymmetric formal, the infinitely many symmetries and their Kac-Moody-Virasoro type algebra structures of the supersymmetric integrable models in higher dimensions can be obtained; .③.Using Painleve analysis, the tests on complete integrability for the supersymmetric integrable models will be performed;.④.We try to find out some new ways for solving supersymmetric integrable models, and then investigate the local excitations and their interactions of the supersymmetric integrable systems..The research work will be helpful to reveal some symmetric structures and essential properties of the supersymmetric integrable systems, and thus can provide a theoretical foundation for the possible physical applications of these supersymmetric integrable models.