A Two-demensional Leznov Lattice Equation With Self-consistent Sources

This paper mainly focused on solving the two-dimensional Leznov lattice equation and a two-dimensional Leznov equation with self-consistent sources. Firstly, by introducing a new dispersion relation we derived the Castorati determinant solution, and then we constructed a new two-dimensional Leznov lattice equation with self-consistent sources and gave its Castorati determinant solution. Secondly, we presented the Gram determinant solution for the two-dimensional Leznov lattice equation and the two-dimensional Leznov equation with self-consistent sources. Finally we gave the Backlund transformation of the two-dimensional Leznov lattice equations with self-consistent sources.