Abstract
In this paper, a special integrable differential-difference equation and its related systems are studied. First of all, by using dependent variable transformations, this special lattice is transformed into two bilinear forms. As a result, the corresponding soliton solutions are obtained. A coupled set of bilinear equations is proposed and related to the same special lattice in a certain way. We also derive the t -flow and z -flow of the coupled bilinear equations. Lax pairs for the t -flow and the z -flow are given. Furthermore, a bilinear Backlund transformation and the corresponding nonlinear superposition formula for the coupled bilinear equations are presented. Soliton solutions to the coupled bilinear equations are derived.
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