作为可积系统理论的一个重要组成部分，超对称可积系统的理论与方法都得到了较大的发展。本项目旨在构造某些超对称可积系统的Darboux变换和Bäcklund变换，以及研究和它们的应用相关的一些问题。. 和经典可积系统中的情况一样，Bäcklund-Darboux变换也是超对称可积系统研究的重要内容。构造超对称可积系统的Bäcklund-Darboux变换，特别是将它们推广到N≥2的超对称系统以及(2+1)-维超对称系统是本项目的一个重要目标。. 另外，本项目着重研究Bäcklund-Darboux变换在超对称可积系统中的应用。内容包括构造超对称可积系统的超孤子解，获得新的超对称半离散、全离散可积系统，构造新的超对称Yang-Baxter映射并探讨其性质。. 通过本项目的研究可以丰富超对称可积系统的理论，对其发展有一定的促进作用。

As an integrated part of the theory of integrable systems,the theory of supersymmetric integrable systems has been greatly developed.The present project aims to construct Bäcklund-Darboux transformations of some supersymmetric integrable systems and consider the applications of Bäcklund-Darboux transformations in the supersymmetric context..Similar to the situation in classical integrable systems,Bäcklund-Darboux transformations are also the important research content of supersymmetric integrable systems.In addition to N=1 supersymmetric systems,the project is meant to construct Bäcklund-Darboux transformations of the N≥2 supersymmetric systems and (2+1)-dimension supersymmetric systems..Furthermore, this project focuses on the applications of Bäcklund-Darboux transformations in the supersymmetric integrable systems.The contents include constructing the supersoliton solutions,obtaining the new supersymmetric semi-discrete and full-discrete systems,constructing the new supersymmetric yang-baxter maps and studying their properties..This research can enrich the theory of supersymmetric integrable systems and promote its development.