Abstract
In this letter, by means of the discrete zero curvature representation, four-component Volterra lattice (FCVL) hierarchy and its first flow, i.e., FCVL system are presented from a 4 × 4 matrix spectral problem with four potential functions. Moreover, a Darboux transformation for the FCVL system is established with the aid of the gauge transformation between the corresponding 4 × 4 matrix spectral problems, by which some exact solutions of the FCVL system are obtained in different cases.
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