On the well-posedness of a nonlocal (two-place) FORQ equation via a two-component peakon system

We investigate the Cauchy problem for a nonlocal (two-place) FORQ equation. By interpreting this equation as special case of two-component peakon system (exhibiting cubic nonlinearity), we convert into ordinary differential equations in Banach space. Using approach, are able to demonstrate local well-posedness Sobolev space Hs where s>5/2. also establish continuity properties data-to-solution map range spaces. Finally, briefly explore relationship between and bi-Hamiltonian AKNS hierarchy.