Explicit Solutions and Conservation Laws for a New Integrable Lattice Hierarchy

الملخص EN

An integrable lattice hierarchy is derived on the basis of a new matrix spectral problem.

Then, some properties of this hierarchy are shown, such as the Liouville integrability, the bi-Hamiltonian structure, and infinitely many conservation laws.

After that, the Darboux transformation of the first integrable lattice equation in this hierarchy is constructed.

Eventually, the explicitly exact solutions of the integrable lattice equation are investigated via graphs.