Darboux transformations and new explicit solutions for the relativistic Volterra lattice

In this paper, Darboux transformations for the relativistic Volterra lattice (RVL) are derived with the help of a gauge transformation of the spectral problem. The determinant representation of n -fold Darboux transformation is established. As an application of the obtained Darboux transformations, new explicit solutions for the RVL are given.