A New Integrable Lattice Hierarchy Associated with a Discrete 3 × 3 Matrix Spectral Problem: N-Fold Darboux Transformation And Explicit Solutions

A new integrable lattice hierarchy is derived from a discrete 3 × 3 matrix spectral problem with three potentials. N-fold Darboux transformation (DT) for a typical lattice equation is constructed basing on its Lax representation, by means of which the explicit solutions in terms of determinant are obtained. Structures of the two- and four-soliton solutions are shown graphically. Inelastic interaction phenomena between/among the two and four solitons are discussed.