New integrable differential-difference systems: Lax pairs, bilinearforms and soliton solutions

Abstract

Two new integrable differential-difference systems with their Lax pairs areproposed. By the dependent variable transformations, these integrable lattices can be transformed into bilinear equations.With the assistance of Mathematica, three-soliton solutions are explicitly obtained. We have also shown that these lattices can be obtained from a special case of the coupled bilinear equationsunder reduction. Furthermore a bilinear Bäcklundtransformation and the corresponding nonlinearsuperposition formula concerning the coupled bilinear equations are presented. Besides, it is also illustrated that the y-flow of these coupled bilinear equationscan be transformed into a latticepreviously derived by the authors.Starting from the corresponding bilinear Bäcklundtransformation, its corresponding Lax pair is obtained.