The multicomponent (2+1)-dimensional Glachette--Johnson (GJ) equation hierarchy and its super-integrable coupling system

This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra \tildeA_M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent (2+1)-dimensional Glachette--Johnson (GJ) hierarchy is given. Finally, the super-integrable coupling system of multicomponent (2+1)-dimensional GJ hierarchy is established through enlarging the spectral problem.