Bäcklund transformations and Lax pairs for two differential-difference equations

Abstract

Two bilinear differential-difference equations are proposed in this paper. The corresponding bilinear Bäcklund transformations (BTs) are presented. Starting from the bilinear BTs, soliton solutions of the proposed equations are generated. By dependent variable transformations, these two equations are transformed into equations in nonlinear variables and the corresponding Lax pairs are derived.