On The Integrable Discrete Versions Of The Leznov Lattice With Self-consistent Sources: Casorati Determinant Solutions

In this paper, by using the “source generation procedure”of Hu Xingbiao etc., anintegrable fully-discrete version and two integrable semi-discrete versions of theLeznov lattice with self-consistent sources are generated from an integrablefully-discrete version and two integrable semi-discrete versions of the Leznov latticewithout self-consistent sources, which arise from the integrable discretization of thetwo-dimensional Leznov lattice. Meanwhile, the Casorati form of the N-solitonsolution for these new equations is presented.