A general method for constructing vector integrable lattice systems

Highlights: • A method for generating vector-value integrable analogies of integrable lattice systems is presented. • Some new vector lattice systems are obtained. • The zero-curvature representations and Hamiltonian structures of the resulting vector lattice systems are formulated. -- Abstract: A method for generating vector-value integrable analogies of integrable lattice systems or integrable differential-difference equations is presented. The basic ingredient of the method is to insert permutation matrices. We formulate the zero-curvature representations and Hamiltonian structures of the resulting vector lattice systems. The effectiveness of the method is illustrated using some examples such as the Volterra lattice, the Belov–Chaltikian lattice, the Ablowitz–Ladik lattice and the Heisenberg ferromagnet lattice.