Double extended cubic peakon equation

• The supersymmetric Novikov equation is defined.
• Two-component and two-peakon generalization of Novikov equation is defined.
• The bi-Hamiltonian system for this generalization is constructed.

In this study, we present the Hamiltonian structure for the supersymmetric N=2N=2 Novikov equation. The bosonic sector gives us a two-component generalization of the cubic peakon equation. We define the double extended cubic peakon equations: two-component and two-peakon Novikov equations. The bi-Hamiltonian structure of this extended system is constructed.