代数几何方法是研究非线性可积系统（拟）周期问题最为有效的工具之一。上个世纪90年代，Gesztesy和Holden进一步发展了代数几何方法并将其成功地用于一大类非线性可积方程族的代数几何解的计算。值得注意的是，所有这些方程都是1+1维的。本项目旨在以Gesztesy和Holden的理论为基础，通过对三个经典的非线性可积系统即Kadomtsev-Petviashvili方程族，2+1维Toda方程和Gross-Pitaevskii 方程的探讨，进一步发展和完善构造高维非线性可积系统代数几何解的新方法。本项目的实施将有效地扩大代数几何方法应用的范围，并为高维非线性可积系统代数几何解及相关问题的研究提供新的手段。

Algebro-geometric method is one of the most effective tools in the study of periodic (quasiperiodic) problems of nonlinear integrable systems. In the 1990s, this method was further developed by Gesztesy and Holden and successfully applied to compute algebro-geometric solutions of a large class of nonlinear integrable hierarchies. Significantly, all these equations are 1+1 dimensional. Based on Gesztesy-Holden's theory, this project aims to develop a new method to construct algebro-geometric solutions for high-dimensional integrable system through discussing three classical equations in nonlinear integrable systems, namely, the Kadomtsev-Petviashvili hierarchy, the 2+1 dimensional Toda lattice and the Gross-Pitaevskii equation. This project will expand the application of algebro-gemetric method, and provide a new way to study algebro-geometric solutions of high-dimensional nonlinear integrable systems and relevant problems.