Conservation laws and self-consistent sources for a super integrable equation hierarchy

In this paper, a super integrable equation hierarchy is considered based on a Lie superalgebra and supertrace identity. Then, a super integrable equation hierarchy with self-consistent sources is established. Furthermore, we introduce two variables F and G to construct conservation laws of the super integrable equation hierarchy and the first two conserved densities and fluxes are listed. It would be specially mentioned that the Fermi variables play an important role in super integrable systems which is different from the ordinary integrable systems.

► Based on the self-consistent sources theory, a super integrable equation hierarchy with self-consistent sources is established.
► We introduce two variables F and G to construct conservation laws of the super integrable equation hierarchy.
► Fermi variables are introduced in super integrable systems.