A New Two-dimensional Toda Lattice Equation With Mixed Self-consistent Sources

The purpose of this paper is to construct a new two-dimensional Toda lattice equation with self-consistent sources and consider its N-soliton solutions in terms of Gram determinant and Casorati determinant by employing the bilinear formalism. By introducing a new dispersion relation, we derive Gram determinant solution and Casorati determinant solution to the two-dimensional Toda lattice equation. Then by applying source generation procedure, we construct a new two-dimensional Toda lattice equation with mixed self-consistent sources and give its Gram-type determinant solution as well as Casorati-type determinant solution. At the end of this paper, the Backlund transformation for the two-dimensional Toda lattice equation with self-consistent sources is derived.