Abstract: Bācklund transformation plays an important role in the study of nonlinear evolution equation. Since to derive the infinitely many conservation laws, the nonlinear superposition formula of solutions and the solution solutions using the Bācklund transformation of some-equation, one often have to use the arbitrary parameters which contained in the Bācklund transformations, so to discuss the relations of the Backlund transformations with different parametres is very important and very useful for the further study of the group structure of the Bācklund transformations. In this paper, we studied the generalized Klein-Gordon equation, the internal wave equation describing a stratified fluid with finite depth and family of the modified Korteweg-de Vries equations in Chern-Peng's operators,and oblained the B_k=L^-1(k)B₁L(k) type decomposition equations.