上世纪七十年代，超对称被引进到可积系统理论中，拓宽了可积性的范围。与经典可积系统分享共同性质的同时，超对称可积系统还表现出一些新颖的性质，这使超对称可积系统有其独特的研究价值。因此，超对称可积系统理论一直是数学物理领域的一个有趣、重要的研究课题。. 本项目涉及三方面的研究内容：第一，利用N=1超对称反向变换产生一些新超对称Harry Dym型方程，并研究它们的可积性质；第二，建立超对称三阶Burgers方程、新超对称五阶KdV方程以及含参数超对称Schr?dinger系统的可积性质，希望得到这些方程的线性谱问题、双线性形式等；第三，基于N=2超对称Harry Dym方程与N=2超对称KdV方程之间的联系，研究N=2超对称方程的反向变换的构造方法，并借助反向变换，研究超对称Harry Dym方程的可积性。

In 1970s, supersymmetry was introduced into the theory of integrable systems, which extensively widened the scope of integrability. Sharing some common features with classical integrable systems, supersymmetric integrable systems also exhibit some novel properties, which distinguish supersymmetric integrable systems from their classical ancestors. Hence, the theory of supersymmetric integrable systems has always been an attractive and important subject in the field of mathematical physics.. This project concerns about three topics. First, we plan to generate some new N=1 supersymmetric integrable systems of Harry Dym type through supersymmetric reciprocal transformation, and to investigate their integrability. Second, the integrability of supersymmetric 3rd order Burgers equation, supersymmetric 5th order KdV equation and supersymmetric Schr?dinger system with a parameter will be investigated, and the linear spectral problems or bilinear forms of these systems are expected to be established. Third, based on the intimate relation between N=2 supersymmetric Harry Dym equations and N=2 supersymmetric KdV equations, we try to propose a general procedure to construct reciprocal transformation for any N=2 supersymmetric equation, and to study integrability of N=2 supersymmetric Harry Dym equations through N=2 supersymmetric reciprocal transformation.