可积系统在流体力学、分子生物学、等离子物理和非线性光学中都有很重要的应用。目前，对普通非线性演化方程的研究已经有很系统的方法，譬如：谱梯度方法、reciprocal 变换方法、Hirota 直接方法等。最近几年超对称可积系统也引起了人们广泛的关注，一些方法也已经被推广到超对称可积系统，然而，还有许多已有的超对称系统的可积性质不完善。另外，相比与普通的非线性演化方程，新的超对称方程仍然很少。我们知道可积系统理论中两个核心问题是：（1） 给定一个非线性方程，判断它是否可积；（2） 找出尽可能多的可积系统。本项目拟在已有工作的基础上，应用谱梯度方法、reciprocal 变换方法和 Hirota 直接方法等针对超对称可积系统展开研究。主要研究包括两个方面：（1） 构造新的超对称可积系统（2）寻找新的超对称系统的可积性质。

The theory of integrable systems plays a prominent role in fluid mechanics, molecular biology, plasma physics and nonlinear optics. Up to now, many methods have been used in nonlinear evolution equations, such as spectral gradient method, reciprocal transformation, Hirota direct method etc. In recent years supersymmetric integrable systems have been studied extensively, some methods have been extended. However, many integrable properties for supersymmetric systems have not been established. Moreover, the new supersymmetric equations remain few. There are two key problems in integrable system theory: (1) it is very important whether a known nonlinear equation has integrable property; (2) find out new equations as many as possible. In this project, we consider supersymmetric systems through spectral gradient method, reciprocal transformation and Hirota direct method. The main contents of this project include two parts: (1) build new supersymmetric integrable systems; (2) find integrable property for new supersymmetric systems.