用规范变换求解(n ,m)^(th)阶KdV系列(英文)

Gauge Transformation to Solve (n,m)^(th) KdV Hierarchy

(n ,m)阶KdV系列是KP系列限制在如 :L[n ,m] =e-mθAe-nθB-1e(n+m)θ 形式的拟微分算子的子流形上所得到的子系列 .本文给出一个构造该系列的规范变换的方法 ,由此可以从其一已知解得到新解 .作为例子 ,详细求解了 ( 1 ,2 )

This paper is mainly to solve (n,m) \%th\%  KdV hierarchy by gauge transformation (GT). The (n,m) \%th\%  KdV hierarchy is a restriction of KP hierarchy to a submanifold of pseudo differential operators as L [n,m] =\%e\% -mθ A\%e\% -nθ B -1 \%e\% (n+m)θ  in a radio form. A method is presented to construct the guage transformation (GT) of (n,m) \%th\%  KdV hierarchy, which keeps the form of the Lax operator. Given an initial solution, many solutions of this hierachy can be obtained. As a example, (1,2) th KdV hierarchy is solved and a new solution of this hierarchy is obtained.