Solving an integrable coupling system of Merola-Ragnisco-Tu lattice equation by Darboux transformation of Lax pair

We research Darboux transformation of Lax pair for an integrable coupling system of the Merola-Ragnisco-Tu lattice equation. Based on the gauge transformation between the Lax pair composed by two triangular systems, a Darboux transformation of the Lax pair is established. As an application of the Darboux transformation, an explicit solution is given.