A new integrable symplectic map for 4-field Blaszak–Marciniak lattice equations

Based on a new discrete 4 × 4 matrix spectral problem, a hierarchy of integrable 4-field Blaszak–Marciniak lattice equations with four potentials is constructed. Moreover, a new integrable symplectic map and its evolutive system of conserved integrals are obtained by the binary nonlinearization of spatial parts and the time parts of Lax pairs and their adjoint Lax pairs of the hierarchy.