Abstract
The transformation by a one parameter group, which is used in an analysis of the nonlinear partial differential equations, is facilitated and is generalized by the concept of the differential perturbation equation. The analysis is as follows. The basic equation is differentiated by a parameter, and this equation is formally solved so as to get the differential equation which involves a parameter-derivative. This is called the differential perturbation equation.
Moreover, when this differential perturbation equation is integrated with respect to a parameter under the appropriate initial condition, the transformation which gives the relation between two solutions of the basic equation is obtained.
This theory is applied to a Bäcklund transformation of Burgers equation and a Cole-Hopf transformation.
