The noncommutative KdV equation and its para-Khler structure

• 作 者: DING Qing HE ZhiZhou
• 机 构: SchoolofMathematicalSciences
• 出 处: 中国科学：数学英文版
• 发表日期: 2014年7期
• 关键词: KdV方程 对位 结构 格拉斯曼流形 交换矩阵 非交换 几何 李代数 para-K?hler structurenoncommutative KdVgeomet
• 基金项目: supported by National Natural Science Foundation of China （Grant No.11271073）,Doctoral Fund of Ministry of Education of China （Grant No.20110071110002）

We prove that the noncommutative(n×n)-matrix KdV equation is exactly a reduction of the geometric KdV flows from R to the symmetric para-Grassmannian manifold G2n,n=SL(2n,R)/SL(n,R)×SL(n,R)and it can also be realized geometrically as a motion of