Transformations from the unperturbed equation to the perturbed equation with nth order perturbation

In this paper, a new algebra method is developed to find the approximate relations between the perturbed nonlinear PDE with nth order perturbation and the unperturbed equation. Through this relations we can transform the unperturbed equation into the perturbed equation with nth order perturbation. This relations include the partial derivatives of the dependent variables with respect to the independent variables. The perturbed KdV equation with second order perturbation serves as example illustrating this fact.