The Darboux Transformation and New Explicit Solutions for the Belov–Chaltikian Lattice

An N-fold Darboux transformation with multi-parameters for the famous Belov–Chaltikian lattice is derived with the aid of the gauge transformation between the corresponding discrete 3×3 matrix spectra. By using the Darboux transformation and the reduction technique, new multi-soliton solutions for the Belov–Chaltikian lattice, which are proved to be of solitary features, are given in the exponential form.