本项目将基于多项式理论和双线性算子性质，发展离散Bell多项式理论及其在离散、超离散和q-差分方程中的应用，在以下三个方面形成突破，做出有自己特色的高水平工作：（1）定义一种离散形式的Bell多项式，并建立其与离散双线性方程之间的联系，从而发展一种可用于构造离散、超离散和q-差分方程的双线性形式、Backlund变换和Lax对的简洁代数方法。（2）通过寻找Bell多项式之间的联系，从而发展另一种构造方程族、Hamilton结构、守恒密度、对称新的代数途径。（3）寻找Bell多项式与其它类型多项式之间的联系，从而发展用其它多项式研究方程的代数方法。本项目研究成果将促进学科交叉，并为可积系统提供新的理论和方法。

Based on theory of polynomials and properties of bilinear operators, this project develops theory of discrete Bell polynomials and its applications to discrete, super-discrete and q-difference equations. We hope make our characteristic and breakthrough work in the following three aspects:（1）By defining a kind of discrete Bell polynomials and establishing its connections with discrete bilinear derivative, we develop a Bell polynomial method to construct bilinear formulization, Backlund transformation and Lax pairs for discrete, super-discrete and q-difference equations. （2）We develop a new discrete Bell polynomial method to construct hierarchy of equations, and their Hamiltonian structures, conservation laws and symmetries. （3）By searching for the connections between Bell polynomial and other polynomials, we hope to develop a new polynomial approach to differential equations. The results of this project will Promote intersect of different subjects and provide new theory and methods for integrable system.