Bilinearization algorithm and KdV- type equations

In this paper , a modification to the basic steps of the bilinearization of evolution equations by Hirota’s method is presented by writing the dependent variable u(x,t) and some of its derivatives almost as Hirota polynomials . Then , a definition to modify Peterson definition for the class of KdV-type equations is presented in addition the general work is illustrated by applications to linear equations and to three classes of the nonlinear well-known equations .