New form (2 + 1)-dimensional integrable lattice hierarchies with two shift operators E˜ and Eˆ

We present a new method to construct two (2 + 1)-dimensional lattice hierarchies. By considering a kind of spectral problems with two shift operators E˜ and Eˆ, a new (2 + 1)-dimensional discrete soliton hierarchy and a new 3×3 lattice hierarchy are constructed by using 3×3 matrix spectral problem.