A three-component differential-difference model: Integrability, Darboux transformation and exact solutions

Abstract A three-component integrable differential-difference dynamic system is introduced. It is interesting that the model includes the modified Volterra lattice, the two-component modified Volterra lattice, the relativistic Volterra lattice and the relativistic Toda lattice as special reductions. In this report, we (I) obtain a Lax pair, (II) use the Lax pair to derive the first three conservations laws, (III) present Darboux transformations. and (IV) construct various kinds of exact solutions.