Odd Hamiltonian structure for supersymmetric Sawada–Kotera equation

We study the supersymmetric N=1N=1 hierarchy connected with the Lax operator of the supersymmetric Sawada–Kotera equation. This operator produces the physical equations as well as the exotic equations with odd time. The odd Bi-Hamiltonian structure for the N=1N=1 supersymmetric Sawada–Kotera equation is defined. The product of the symplectic and implectic Hamiltonian operator gives us the recursion operator. In that way we prove the integrability of the supersymmetric Sawada–Kotera equation in the sense that it has the Bi-Hamiltonian structure. The so-called “quadratic” Hamiltonian operator of even order generates the exotic equations while the “cubic” odd Hamiltonian operator generates the physical equations.