连续和离散模型的精确解及可积性一直是现代数学物理核心研究课题之一，精确解可用于解释已知的物理实验现象、揭示物理机制并预测未来的发展，而可积性可以在一定程度上为解提供信息。随着计算物理和理论物理发展的日益完善，从多种角度研究非线性数学物理方程的性质越来越受到重视。本项目主要研究: A) 研究连续、离散方程的非局域对称，并构造方程的精确解、守恒律、可积梯队； B) 利用保对称离散算法研究高维非线性数学物理方程的离散格式，并推广到可积离散格式。这将得到具有实际物理背景的椭圆周期波和孤立波相互作用等奇异性波解, 产生新的可积离散系统，为数学物理的研究提供新的途径。

One of the central topics in modern mathematical physics is to find exact solution and integrability of the continuous and discrete models. Exact solutions can be used to explain the known physical experiment phenomena, the physical mechanism and predict the future development, while integrability can provide some information on the solution. With the development of computational physics and theory physics, the study on properties of the nonlinear mathematical physics equation from a variety of perspective is more and more attention. In this project we will mainly focus on: A) Study on nonlocal symmetry of continuous and discrete equations, construct the exact solutions, conservation laws, integrable hierarchies of the equations. B) Using the symmetry-preserving scheme to study the discrete formats of some high dimensional nonlinear mathematical physics equations, and extended to the integrable discrete format. This will lead to a kind of interaction solutions among elliptic periodic waves and solitons, generate new integrable discrete systems, which provides a new way for the research of mathematical physics.