带自相容源KdV、mKdV和Harry Dym方程之间的Bcklund变换

Bcklund Transformations Between KdV Equation and mKdV Equation with Self-consistent Sources,mKdV Equation and Harry Dym Equation with Self-consistent Sources

在Sato理论的框架下,利用拟微分算子探讨了1+1维带源可积方程族之间的Bcklund变换,构造了带源Kd V方程与带源mKdV方程、带源mKdV方程和带源Harry Dym方程之间的Bcklund变换,结果表明,在所构造的Bcklund变换作用下,第一(二)型标准的带源KdV、mKdV方程分别变换成非标准的第一(二)型的带源mKdV、Harry Dym方程。

Backlund transformations between 1＋1 dimensional integrable hierarchies by the pseudo-dif-ferential operator in the framework of Sato theory are discussed. Backlund transformation between KdV equa-tion with self-consistent sources （with sources） and mKdV equation with sources, mKdV equation with sources and Harry Dym equation with sources are given, respectively. The results show that under the Backlund transformation, the first （two） standard type of KdV, mKdV equation with sources are transformed into the first （two） non-standard type of mKdV, Harry Dym equation with sources, respectively.