Study Of Some Problems Of Noncommutative Integrable Equation

We derived various noncommutative integrable equations by the Lax-Pair generating technique and the Sato theory and we also show the existence of corresponding hierarchy in this paper, the existence of the hierarchy suggest a hidden infinite-dimensional symmetry in the noncommutative Lax equations. We show that NC KdV equation could be derived from a noncommutative self-dual Yang-Mills equation by reduction. We derived the con-served quantities of the noncommutative Burgers equation by the bi-complex method. We finally show that a noncommutative Burgers equation is linearizable via noncommutative Cole-Hopf transformation, so we show the integrability of the equation.