A similar extension of the WKI hierarchy, its Hamiltonian structure and the associated finite-dimensional Hamiltonian system

An isospectral problem and a similar extension of the Wadati–Konno–Ichikawa hierarchy are proposed. By using the trace identity, it is shown that the hierarchy of equations possesses a bi-Hamiltonian structure. The eigenvalue problem is nonlinearized to a finite-dimensional Hamiltonian system under a constraint between the potentials and the eigenfunctions.