孤立子方程

By finding symmetries ,group- invariant solutions and reducing equations, we dig out integrable system and then obtain accurate solutions for nonlinear differential equations appearing in physics-mathematics field. By Painleve.analysis ，and then getting B.cklund transformations, we obtain formulas for.accurate solutions . By using some ways and conclusions in solition theories，.systematic discussions have been put on B.cklund transformation on Wargarten.surface in Euclidean space R3 and Minkovski space R2,1 .By using computer, some new intrgrable systems and symmetries in equations have been found. These works have been finished according our plan. 16 papers (domestic:5 international:11) have.appeared and one book named Lie group and its applications to differential.equations has been published (Scientific Publishing House, Bejing) .

对物理和几何中的一些非线性问题，可积系统或非可积系统，研究它们的有关对称、不变群以及Backlund变换等理论，寻找方程的精确解。不仅将微分几何和变换群等工具应用于孤立子方程的研究，而且将孤立子理论研究中的方法和结果应用于微分几何中的一些非线性问题。此外，还借助计算机符号运算寻找新的可积系统和方程的解析介。