摘要
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 Sym-Pohlmeyer curves in the symmetric Lie algebra sl(2n,R)with initial data being suitably restricted.This gives a para-geometric characterization of the noncommutative matrix KdV equation.
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 Sym-Pohlmeyer curves in the symmetric Lie algebra sl（2n,R） with initial data being suitably restricted.This gives a para-geometric characterization of the noncommutative matrix KdV equation.
基金
supported by National Natural Science Foundation of China (Grant No.11271073)
Doctoral Fund of Ministry of Education of China (Grant No.20110071110002)
