A Darboux transformation of the sl(2|1)sl(2|1) super KdV hierarchy and a super lattice potential KdV equation

• The hierarchy of super sl(2|1)sl(2|1) KdV equations is derived.
• Each equation in the hierarchy is shown to be bi-super-Hamiltonian.
• The Holod–Pakuliak super KdV equation is a member of the hierarchy.
• A Darboux transformation of the hierarchy is constructed.
• A super lattice potential KdV (lpKdV) equation with two discrete variables is obtained.

A hierarchy of super KdV equations is derived from sl(2|1)sl(2|1) supermatrix-valued spectral problem. Each equation in the hierarchy is shown to be bi-super-Hamiltonian. Moreover, a Darboux transformation of the hierarchy is constructed. As the compatibility condition of a pair of the Darboux transformations, we obtain a super lattice potential KdV (lpKdV) equation with two discrete variables.