Symmetries and conservation laws of lattice Boussinesq equations

► Symmetries and conservation laws for lattice Boussinesq system are constructed. ► Corresponding results for lattice modified Boussinesq system are presented. ► The generating PDE (GPDE) for lattice modified Boussinesq is derived. ► Lax pair and Bäcklund transformation for this GPDE are explicitly given.