上世纪七十年代末，超对称被引入可积系统理论中。这两个“不相关”的理论的结合，一方面极大地拓展了可积性的研究范围；另一方面为数学、物理中的超对象提供更多展示其作用的机会。超对称可积系统表现出的新颖性质使其独立于经典可积系统、赋予它们独特的研究价值。.本项目涉及两方面的研究内容：其一，我们将借助master对称研究一些超对称方程的可积性，包括超对称三阶Burgers方程、超对称五阶Korteweg-de Vries方程和超对称Camassa-Holm方程等；其二，系统研究超对称零曲率方程和Cartan-Maurer方程，以建立超对称Kaup-Newell和Wadati-Konno-Ichikawa谱问题理论。

The supersymmetry was introduced into the theory of integrable systems in late seventies of last century. Such combination of two seemingly irrelevant theories extensively widens the scope of integrability on the one hand, and provides super objects with more opportunities to exercise influence over both mathematics and physics on the other hand. The novel properties exhibited by supersymmetric (SUSY) integrable systems distinguish them from their classical ancestors and endow them with special value. .This project concerns two topics. On the one hand, we plan to investigate integrability of some supersymmetric equations through master symmetries, including SUSY third order Burgers equation, SUSY fifth order Korteweg-de Vries equation, SUSY Camassa-Holm equation etc. On the other hand, the SUSY zero curvature equation and Cartan-Maurer equation will be systematically studied to establish supersymmetric counterparts of the Kaup-Newell and Wadati-Konno-Ichikawa spectral problems.