A non-isospectral integrable couplings of Volterra lattice hierarchy with self-consistent sources

A kind of non-isospectral integrable couplings of discrete soliton equations hierarchy with self-consistent sources associated with sl˜(4) [Y.F. Zhang, E.G. Fan, Characteristic Numbers of Matrix Lie Algebras, Commun. Theor. Phys (China) 49 (2008) 845] is presented. As an application example, the hierarchy of non-isospectral cubic Volterra lattice hierarchy with self-consistent sources is derived. Furthermore, we construct a non-isospectral integrable couplings of cubic Volterra lattice hierarchy with self-consistent sources by using the loop algebra sl˜(4).