Abstract
The auto-Bäcklund transformation of KdV equation can be constructed by the solution of the Differential Perturbation Equation (abrivated by DPE), which is an extension of Lie's equation. Therefore, it is considered that the auto-Bäcklund transformations of the various integrable equations will be obtained in terms of DPE.
Furthermore, the multi-parameter DPE is introduced. One of its applications is the recursion operator, which is initiated by P. J. Olver. And the multi-parameter DPEs of Burgers equation are derived.
In particular, the concept “multi-parameter DPE” corresponds to the generalization of invariant surfaces which are suggested by S. Kumei.
